# kb

id: sums-of-powers-20260505-0
file: data/en.wikipedia.org/wiki/Sums_of_powers-0.md
category: reference
title: Sums of powers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sums_of_powers
date_saved: 2026-05-05T08:17:23.640704+00:00
instance: kb-cron
parent: sums-of-powers-20260505-0
summary:
In mathematics and statistics, sums of powers occur in a number of contexts: Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities. There are only finitely many positive integers that are not sums of distinct squares. The largest one is 128. The same applies for sums of distinct cubes (largest one is 12,758), distinct fourth powers (largest is 5,134,240), etc. See for a generalization to sums of polynomials. Faulhaber's formula expresses 1 k + 2 k + 3 k + ⋯ + n k {\displaystyle 1^{k}+2^{k}+3^{k}+\cdots +n^{k}} as a polynomial in n, or alternatively in terms of a Bernoulli polynomial. Fermat's right triangle theorem states that there is no solution in positive integers for a 2 = b 4 + c 4 {\displaystyle a^{2}=b^{4}+c^{4}} and a 4 = b 4 + c 2 {\displaystyle a^{4}=b^{4}+c^{2}} . Fermat's Last Theorem states that x k + y k = z k {\displaystyle x^{k}+y^{k}=z^{k}} is impossible in positive integers with k > 2. The equation of a


id: list-of-sums-of-reciprocals-20260505-0
file: data/en.wikipedia.org/wiki/List_of_sums_of_reciprocals-0.md
category: reference
title: List of sums of reciprocals
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_sums_of_reciprocals
date_saved: 2026-05-05T08:17:27.040927+00:00
instance: kb-cron
parent: list-of-sums-of-reciprocals-20260505-0
summary:
In mathematics and number theory, the sum of reciprocals (or sum of inverses) is defined as the sum of reciprocals of some series of positive integers (counting numbers). It is a sum of unit fractions. If infinitely many numbers have their reciprocals summed, generally the terms are given as a sequence whose nth term is defined as the sum of the first n reciprocals. For sums of reciprocals over a series of finitely many numbers, key questions include whether there is a simple expression for the value of the sum, whether the sum must be less than a certain value, and whether the sum is ever an integer. When the sum of reciprocals is over an infinite series, questions include: First, does the sequence of sums diverge—that is, does it eventually exceed any given number—or does it converge, meaning there is some number that it gets arbitrarily close to without ever exceeding it? (A set of positive integers is said to be large if the sum of its reciprocals diverges, and small if it converges.) Second, if it converges, what is a simple expression for the value it converges to? Is that value rational or irrational, and is that value


id: list-of-sums-of-reciprocals-20260505-1
file: data/en.wikipedia.org/wiki/List_of_sums_of_reciprocals-1.md
category: reference
title: List of sums of reciprocals
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_sums_of_reciprocals
date_saved: 2026-05-05T08:17:27.040927+00:00
instance: kb-cron
parent: list-of-sums-of-reciprocals-20260505-0
summary:
A sum-free sequence of increasing positive integers is one for which no number is the sum of any subset of the previous ones. The sum of the reciprocals of the numbers in any sum-free sequence is less than 2.8570 . The sum of the reciprocals of the heptagonal numbers converges to a known value that is not only irrational but also transcendental, and for which there exists a complicated formula. The sum of the reciprocals of the twin primes, of which there may be finitely many or infinitely many, is known to be finite and is called Brun's constant, approximately 1.90216 . (By convention, the reciprocal of 5 {\displaystyle 5} appears twice in the sum.) The sum of the reciprocals of the Proth primes, of which there may be finitely many or infinitely many, is known to be finite, approximately 0.747392479 . The prime quadruplets are pairs of twin primes with only one odd number between them. The sum of the reciprocals of the numbers in prime quadruplets is approximately 0.8706 . The sum of the reciprocals of the perfect powers (including duplicates) is 1 . The sum of the reciprocals of the perfect powers (excluding duplicates) is approximately 0.8745


id: list-of-sums-of-reciprocals-20260505-2
file: data/en.wikipedia.org/wiki/List_of_sums_of_reciprocals-2.md
category: reference
title: List of sums of reciprocals
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_sums_of_reciprocals
date_saved: 2026-05-05T08:17:27.040927+00:00
instance: kb-cron
parent: list-of-sums-of-reciprocals-20260505-0
summary:
=== Divergent series === The n-th partial sum of the harmonic series, which is the sum of the reciprocals of the first n positive integers, diverges as n goes to infinity, albeit extremely slowly: The sum of the first 1043 terms is less than 100 . The difference between the cumulative sum and the natural logarithm of n converges to the Euler–Mascheroni constant, commonly denoted as γ , {\displaystyle \gamma ,} which is approximately 0.5772. The sum of the reciprocals of the primes diverges. Given coprime positive integers a and b, the sum of the reciprocal of the primes of the form an + b diverges. This result is used to prove the Dirichlet's theorem, which states that there are infinitely many primes p {\displaystyle p} satisfying p ≡ a ( m o d b ) {\displaystyle p\equiv a{\text{ }}(\mathrm {mod} {\text{ }}b)} . The sum of the reciprocals of the primes of the form 4n + 1 is divergent. By Fermat's theorem on sums of two squares, it follows that the sum of reciprocals of numbers of the form a 2 + b 2 , {\displaystyle a^{2}+b^{2},} where a and b are non-negative integers, not both equal to 0,


id: table-of-mathematical-symbols-by-introduction-date-20260505-0
file: data/en.wikipedia.org/wiki/Table_of_mathematical_symbols_by_introduction_date-0.md
category: reference
title: Table of mathematical symbols by introduction date
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Table_of_mathematical_symbols_by_introduction_date
date_saved: 2026-05-05T08:17:28.247985+00:00
instance: kb-cron
parent: table-of-mathematical-symbols-by-introduction-date-20260505-0
summary:
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. == See also == History of mathematical notation History of the Hindu–Arabic numeral system Glossary of mathematical symbols List of mathematical symbols by subject Mathematical notation Mathematical operators and symbols in Unicode == Sources == == External links == RapidTables: Math Symbols List Jeff Miller: Earliest Uses of Various Mathematical Symbols


id: list-of-types-of-systems-theory-20260505-0
file: data/en.wikipedia.org/wiki/List_of_types_of_systems_theory-0.md
category: reference
title: List of types of systems theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_types_of_systems_theory
date_saved: 2026-05-05T08:17:29.461574+00:00
instance: kb-cron
parent: list-of-types-of-systems-theory-20260505-0
summary:
This list of types of systems theory gives an overview of different types of systems theory, which are mentioned in scientific book titles or articles. The following more than 40 types of systems theory are all explicitly named systems theory and represent a unique conceptual framework in a specific field of science. Systems theory has been formalized since the 1950s, and a long set of specialized systems theories and cybernetics exist. In the beginnings, general systems theory was developed by Ludwig von Bertalanffy to overcome the over-specialisation of the modern times and as a worldview using holism. The systems theories nowadays are closer to the traditional specialisation than to holism, by interdependencies and mutual division by mutually-different specialists. == A == Abstract systems theory (also see: formal system) Action Theory Adaptive systems theory (also see: complex adaptive system) Applied general systems theory (also see: general systems theory) Applied multidimensional systems theory Archaeological systems theory (also see: Systems theory in archaeology) Systems theory in anthropology Associated systems theory == B == Behavioral systems theory Biochemical systems theory Biomatrix systems theory Body system == C == Complex adaptive systems theory (also see: complex adaptive system) Complex systems theory (also see: complex systems)


id: tarjan-s-algorithm-20260505-0
file: data/en.wikipedia.org/wiki/Tarjan's_algorithm-0.md
category: reference
title: Tarjan's algorithm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Tarjan's_algorithm
date_saved: 2026-05-05T08:17:30.674857+00:00
instance: kb-cron
parent: tarjan-s-algorithm-20260505-0
summary:
Tarjan's algorithm may refer to one of several algorithms attributed to Robert Tarjan, including: Tarjan's strongly connected components algorithm Tarjan's off-line lowest common ancestors algorithm Tarjan's algorithm for finding bridges in an undirected graph Tarjan's algorithm for finding simple circuits in a directed graph == See also == List of algorithms == References ==


id: list-of-tessellations-20260505-0
file: data/en.wikipedia.org/wiki/List_of_tessellations-0.md
category: reference
title: List of tessellations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_tessellations
date_saved: 2026-05-05T08:17:31.940951+00:00
instance: kb-cron
parent: list-of-tessellations-20260505-0
summary:
This is a list of tessellations. == Spherical == == Planar == == Hyperbolic == == See also == Tessellation Uniform tiling Convex uniform honeycombs List of k-uniform tilings List of Euclidean uniform tilings Uniform tilings in hyperbolic plane == References ==


id: list-of-theorems-20260505-0
file: data/en.wikipedia.org/wiki/List_of_theorems-0.md
category: reference
title: List of theorems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_theorems
date_saved: 2026-05-05T08:17:33.142978+00:00
instance: kb-cron
parent: list-of-theorems-20260505-0
summary:
This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures List of data structures List of derivatives and integrals in alternative calculi List of equations List of fundamental theorems List of hypotheses List of inequalities Lists of integrals List of laws List of lemmas List of limits List of logarithmic identities List of mathematical functions List of mathematical identities List of mathematical proofs List of misnamed theorems List of scientific laws List of theories Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields. == Logics and foundations == Ax–Grothendieck theorem (model theory) Barwise compactness theorem (mathematical logic) Borel determinacy theorem (set theory) Büchi-Elgot-Trakhtenbrot theorem (mathematical logic) Cantor–Bernstein–Schröder theorem (set theory, cardinal numbers) Cantor's theorem (set theory) Church–Rosser theorem (lambda calculus) Compactness theorem (mathematical logic) Conservativity theorem (mathematical logic) Craig's theorem (mathematical logic) Craig's interpolation theorem (mathematical logic) Cut-elimination theorem (proof theory) Deduction theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set theory) Feferman–Vaught theorem (model theory) Friedberg–Muchnik theorem (mathematical logic) Fundamental theorem of equivalence relations


id: list-of-theorems-20260505-1
file: data/en.wikipedia.org/wiki/List_of_theorems-1.md
category: reference
title: List of theorems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_theorems
date_saved: 2026-05-05T08:17:33.142978+00:00
instance: kb-cron
parent: list-of-theorems-20260505-0
summary:
== Number theory == 15 and 290 theorems (number theory) Albert–Brauer–Hasse–Noether theorem (algebras) Ankeny–Artin–Chowla theorem (number theory) Apéry's theorem (number theory) Artin–Verdier duality theorem (number theory) ATS theorem (number theory) Auxiliary polynomial theorem (Diophantine approximation) Ax–Kochen theorem (number theory) Baker's theorem (number theory) Barban–Davenport–Halberstam theorem (analytic number theory) Basel problem (mathematical analysis) Beatty's theorem (Diophantine approximation) Behrend's theorem (number theory) Bertrand's postulate (number theory) Birch's theorem (algebraic number theory) Bombieri's theorem (number theory) Bombieri–Friedlander–Iwaniec theorem (number theory) Brauer–Siegel theorem (number theory) Brun's theorem (number theory) Brun–Titchmarsh theorem (number theory) Carmichael's theorem (Fibonacci numbers) Chebotarev's density theorem (number theory) Chen's theorem (number theory) Chowla–Mordell theorem (number theory) Cohn's irreducibility criterion (polynomials) Critical line theorem (number theory) Davenport–Schmidt theorem (number theory, Diophantine approximations) Dirichlet's approximation theorem (Diophantine approximations) Dirichlet's theorem on arithmetic progressions (number theory) Dirichlet's unit theorem (algebraic number theory) Equidistribution theorem (ergodic theory) Erdős–Kac theorem (number theory) Euclid's theorem (number theory) Euclid–Euler theorem (number theory) Euler's theorem (number theory) Fermat's Last Theorem (number theory) Fermat's little theorem (number theory) Fermat's theorem on sums of two squares (number theory) Ferrero–Washington theorem (algebraic number theory) Ford's theorem (number theory) Franel–Landau theorem (number theory) Gelfond–Schneider theorem (transcendental number theory) Glaisher's theorem (number theory)


id: list-of-theorems-20260505-2
file: data/en.wikipedia.org/wiki/List_of_theorems-2.md
category: reference
title: List of theorems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_theorems
date_saved: 2026-05-05T08:17:33.142978+00:00
instance: kb-cron
parent: list-of-theorems-20260505-0
summary:
== Linear and multilinear algebra; matrix theory == Amitsur–Levitzki theorem (linear algebra) Binomial inverse theorem (linear algebra) Birkhoff–Von Neumann theorem (linear algebra) Bregman–Minc inequality (discrete mathematics) Cauchy-Binet formula (linear algebra) Cayley–Hamilton theorem (Linear algebra) Dimension theorem for vector spaces (vector spaces, linear algebra) Euler's rotation theorem (geometry) Exchange theorem (linear algebra) Gamas's Theorem (multilinear algebra) Gershgorin circle theorem (matrix theory) Inverse eigenvalues theorem (linear algebra) Perron–Frobenius theorem (matrix theory) Principal axis theorem (linear algebra) Rank–nullity theorem (linear algebra) Rouché–Capelli theorem (Linear algebra) Sinkhorn's theorem (matrix theory) Specht's theorem (matrix theory) Spectral theorem (linear algebra, functional analysis) Sylvester's determinant theorem (determinants) Sylvester's law of inertia (quadratic forms) Witt's theorem (quadratic forms) == Associative rings and algebras == Artin–Wedderburn theorem (abstract algebra) Artin–Zorn theorem (algebra) Brauer–Cartan–Hua theorem (ring theory) Frobenius theorem (abstract algebras) Goldie's theorem (ring theory) Jacobson density theorem (ring theory) Jacobson–Bourbaki theorem (algebra) Levitzky's theorem (ring theory) Regev's theorem (ring theory) Skolem–Noether theorem (simple algebras) Wedderburn's little theorem (ring theory) Wedderburn's theorem (abstract algebra) == Nonassociative rings and algebras == Ado's theorem (Lie algebra) Goddard–Thorn theorem (vertex algebras) Hurwitz's theorem (normed division algebras) Jacobson–Morozov theorem (Lie algebra) Levi's theorem (Lie groups) Lie's theorem (Lie algebra) Poincaré–Birkhoff–Witt theorem (universal enveloping algebras)


id: list-of-theorems-20260505-3
file: data/en.wikipedia.org/wiki/List_of_theorems-3.md
category: reference
title: List of theorems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_theorems
date_saved: 2026-05-05T08:17:33.142978+00:00
instance: kb-cron
parent: list-of-theorems-20260505-0
summary:
== Functions of a complex variable == Akhiezer's theorem (complex analysis) Arakelyan's theorem (complex analysis) Area theorem (conformal mapping) (complex analysis) Beurling–Lax theorem (Hardy spaces) Bloch's theorem (complex analysis) Bôcher's theorem (complex analysis) Borel–Carathéodory theorem (complex analysis) Branching theorem (complex manifold) Carathéodory's theorem (complex analysis) Carleson–Jacobs theorem (complex analysis) Carlson's theorem (complex analysis) Cauchy integral theorem (complex analysis) Cauchy–Hadamard theorem (complex analysis) Clifford's theorem on special divisors (algebraic curves) Corona theorem (complex analysis) de Branges's theorem (complex analysis) De Franchis theorem (Riemann surfaces) Edge-of-the-wedge theorem (complex analysis) Farrell–Markushevich theorem (complex analysis) Fatou's theorem (complex analysis) Fundamental theorem of algebra (complex analysis) Gauss–Lucas theorem (complex analysis) Grunsky's theorem (complex analysis) Hadamard three-circle theorem (complex analysis) Hadamard three-lines theorem (complex analysis) Hardy's theorem (complex analysis) Hartogs–Rosenthal theorem (complex analysis) Harnack's theorem (complex analysis) Hurwitz's automorphisms theorem (algebraic curves) Hurwitz's theorem (complex analysis) Identity theorem (complex analysis) Identity theorem for Riemann surfaces (Riemann surfaces) Koebe 1/4 theorem (complex analysis) Lagrange inversion theorem (mathematical analysis, combinatorics) Lagrange reversion theorem (mathematical analysis, combinatorics) Laurent expansion theorem (complex analysis) Lindelöf's theorem (complex analysis) Liouville's theorem (complex analysis, entire functions) Liouville's theorem (conformal mappings) Looman–Menchoff theorem (complex analysis) Marden's theorem (polynomials) Mergelyan's theorem (complex analysis) Measurable Riemann


id: list-of-theorems-20260505-4
file: data/en.wikipedia.org/wiki/List_of_theorems-4.md
category: reference
title: List of theorems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_theorems
date_saved: 2026-05-05T08:17:33.142978+00:00
instance: kb-cron
parent: list-of-theorems-20260505-0
summary:
== Operator theory == Aronszajn–Smith theorem (functional analysis) Atiyah–Singer index theorem (elliptic differential operators, harmonic analysis) Atkinson's theorem (operator theory) Babuška–Lax–Milgram theorem (partial differential equations) Banach–Stone theorem (operator theory) Bauer–Fike theorem (spectral theory) Bounded inverse theorem (operator theory) Browder–Minty theorem (operator theory) Choi's theorem on completely positive maps (operator theory) Commutation theorem (von Neumann algebra) Fuglede's theorem (functional analysis) Gelfand–Mazur theorem (Banach algebra) Gelfand–Naimark theorem (functional analysis) Hardy–Littlewood maximal theorem (real analysis) Hellinger–Toeplitz theorem (functional analysis) Hilbert–Schmidt theorem (functional analysis) Hille–Yosida theorem (functional analysis) Kaplansky density theorem (von Neumann algebra) Kuiper's theorem (operator theory, topology) Lax–Milgram theorem (partial differential equations) Lions–Lax–Milgram theorem (partial differential equations) Lumer–Phillips theorem (semigroup theory) Marcinkiewicz theorem (functional analysis) Mazur–Ulam theorem (normed spaces) Mercer's theorem (functional analysis) Min-max theorem (functional analysis) Moreau's theorem (convex analysis) Nash–Moser theorem (mathematical analysis) Open mapping theorem (functional analysis) Peetre theorem (functional analysis) Riesz–Thorin theorem (functional analysis) Ryll-Nardzewski fixed-point theorem (functional analysis) Sazonov's theorem (functional analysis) Schröder–Bernstein theorems for operator algebras (operator algebras) Stinespring factorization theorem (operator theory) Stone's theorem on one-parameter unitary groups (functional analysis) Sz.-Nagy's dilation theorem (operator theory) Tomita's theorem (operator algebras) Von Neumann bicommutant theorem (functional analysis) Von Neumann's theorem (operator theory) == Calculus of variations and


id: list-of-theorems-20260505-5
file: data/en.wikipedia.org/wiki/List_of_theorems-5.md
category: reference
title: List of theorems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_theorems
date_saved: 2026-05-05T08:17:33.142978+00:00
instance: kb-cron
parent: list-of-theorems-20260505-0
summary:
== General topology == Arzelà–Ascoli theorem (functional analysis) Baire category theorem (topology, metric spaces) Bing metrization theorem (general topology) Bolzano–Weierstrass theorem (real analysis, calculus) Borsuk–Ulam theorem (topology) Brouwer fixed-point theorem (topology) Cantor's intersection theorem (real analysis) Closed graph theorem (functional analysis) Extreme value theorem (calculus) Fixed-point theorems in infinite-dimensional spaces Hairy ball theorem (algebraic topology) Hahn–Mazurkiewicz theorem (continuum theory) Heine–Borel theorem (real analysis) Heine–Cantor theorem (metric geometry) Jordan curve theorem (topology) Kuratowski's closure-complement problem (topology) Lebesgue covering dimension (dimension theory) Metrization theorems (topological spaces) Nagata–Smirnov metrization theorem(general topology) Netto's theorem (topology) Parovicenko's theorem (topology) Tietze extension theorem (general topology) Tychonoff's theorem (general topology) == Algebraic topology == Acyclic models theorem (algebraic topology) Blakers–Massey theorem (homotopy theory) Bott periodicity theorem (homotopy theory) Brown's representability theorem (homotopy theory) Cellular approximation theorem (algebraic topology) Dold–Thom theorem (algebraic topology) Eilenberg–Ganea theorem (homological algebra, algebraic topology) Eilenberg–Zilber theorem (algebraic topology) Euler's polyhedron theorem (polyhedra) Excision theorem (homology theory) Freudenthal suspension theorem (homotopy theory) Hilton–Milnor theorem (algebraic topology) Homotopy excision theorem (algebraic topology) Hopf theorem (differential topology) Hurewicz theorem (algebraic topology) Künneth theorem (algebraic topology) Invariance of domain (algebraic topology) Landweber exact functor theorem (algebraic topology) Lefschetz fixed-point theorem (fixed points, algebraic topology) Lefschetz–Hopf theorem (topology)


id: list-of-theorems-20260505-6
file: data/en.wikipedia.org/wiki/List_of_theorems-6.md
category: reference
title: List of theorems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_theorems
date_saved: 2026-05-05T08:17:33.142978+00:00
instance: kb-cron
parent: list-of-theorems-20260505-0
summary:
== Mechanics of deformable solids == Betti's theorem (physics) Castigliano's first and second theorems (structural analysis) Clapeyron's theorem (physics) Saint-Venant's theorem (physics) Theorem of three moments (physics) == Fluid mechanics == Buckingham π theorem (dimensional analysis) Helmholtz's theorems (physics) Kelvin's circulation theorem (physics) Kutta–Joukowski theorem (physics) Reynolds transport theorem (fluid dynamics) Taylor–Proudman theorem (physics) == Optics, electromagnetic theory == Blondel's theorem (electric power) (physics) Earnshaw's theorem (electrostatics) Maximum power theorem (electrical circuits) Norton's theorem (electrical networks) Optical theorem (physics) Poynting's theorem (physics) Thévenin's theorem (electrical circuits) == Classical thermodynamics, heat transfer == Carnot's theorem (thermodynamics) Clausius theorem (physics) == Quantum theory == Adiabatic theorem (physics) Bell's theorem (quantum mechanics) Bogoliubov–Parasyuk theorem (quantum field theory) Byers–Yang theorem (quantum mechanics) C-theorem (physics) Cluster decomposition theorem (quantum field theory) Coleman–Mandula theorem (quantum field theory) Elitzur's theorem (quantum field theory, statistical field theory) Furry's theorem (quantum field theory) Gell-Mann and Low theorem (quantum field theory) Gleason's theorem (Hilbert space) Goldstone's theorem (physics) Haag's theorem (quantum field theory) Haag–Łopuszański–Sohnius theorem (physics) Hellmann–Feynman theorem (physics) Kinoshita–Lee–Nauenberg theorem (quantum field theory) Kochen–Specker theorem (physics) Kramers' theorem (physics) Nielsen–Ninomiya theorem (quantum field theory) No-broadcasting theorem (quantum information theory) No-cloning theorem (quantum computation) No-communication theorem (quantum information theory) No-deleting


id: list-of-theorems-called-fundamental-20260505-0
file: data/en.wikipedia.org/wiki/List_of_theorems_called_fundamental-0.md
category: reference
title: List of theorems called fundamental
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_theorems_called_fundamental
date_saved: 2026-05-05T08:17:34.373025+00:00
instance: kb-cron
parent: list-of-theorems-called-fundamental-20260505-0
summary:
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus. The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory. Some of these are classification theorems of objects which are mainly dealt with in the field. For instance, the fundamental theorem of curves describes classification of regular curves in space up to translation and rotation. Likewise, the mathematical literature sometimes refers to the fundamental lemma of a field. The term lemma is conventionally used to denote a proven proposition which is used as a stepping stone to a larger result, rather than as a useful statement in-and-of itself. == Fundamental theorems of mathematical topics == Fundamental theorem of algebra Fundamental theorem of algebraic K-theory Fundamental theorem of arithmetic Fundamental theorem of Boolean algebra Fundamental theorem of calculus Fundamental theorem of calculus for line integrals Fundamental theorem of curves Fundamental theorem of cyclic groups Fundamental theorem of dynamical systems Fundamental theorem of equivalence relations Fundamental theorem of exterior calculus Fundamental theorem


id: list-of-misnamed-theorems-20260505-0
file: data/en.wikipedia.org/wiki/List_of_misnamed_theorems-0.md
category: reference
title: List of misnamed theorems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_misnamed_theorems
date_saved: 2026-05-05T08:17:35.596362+00:00
instance: kb-cron
parent: list-of-misnamed-theorems-20260505-0
summary:
This is a list of misnamed theorems in mathematics. It includes theorems (and lemmas, corollaries, conjectures, laws, and perhaps even the odd object) that are well known in mathematics, but which are not named for the originator. That is, the items on this list illustrate Stigler's law of eponymy (which is not, of course, due to Stephen Stigler, who credits Robert K Merton). == Applied mathematics == Benford's law. This was first stated in 1881 by Simon Newcomb, and rediscovered in 1938 by Frank Benford. The first rigorous formulation and proof seems to be due to Ted Hill in 1988.; see also the contribution by Persi Diaconis. Bertrand's ballot theorem. This result concerning the probability that the winner of an election was ahead at each step of ballot counting was first published by W. A. Whitworth in 1878, but named after Joseph Louis François Bertrand who rediscovered it in 1887. A common proof uses André's reflection method, though the proof by Désiré André did not use any reflections. == Algebra == Burnside's lemma. This was stated and proved without attribution in Burnside's 1897 textbook, but it had previously been discussed by Augustin Cauchy, in 1845, and by Georg Frobenius in


id: list-of-misnamed-theorems-20260505-1
file: data/en.wikipedia.org/wiki/List_of_misnamed_theorems-1.md
category: reference
title: List of misnamed theorems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_misnamed_theorems
date_saved: 2026-05-05T08:17:35.596362+00:00
instance: kb-cron
parent: list-of-misnamed-theorems-20260505-0
summary:
== Number theory == Bézout's theorem. The statement may have been made first by Isaac Newton in 1665. The matter of a proof was taken up by Colin MacLaurin (c. 1720) and Leonhard Euler as well as Étienne Bézout (c. 1750). However, Bézout's "proof" was incorrect. The first correct proof seems to be due mostly to Georges-Henri Halphen in the 1870s. Cramer's rule. It is named after Gabriel Cramer (1704–1752), who published the rule in his 1750 Introduction à l'analyse des lignes courbes algébriques, although Colin Maclaurin also published the method in his 1748 Treatise of Algebra (and probably knew of the method as early as 1729). Pell's equation. The solution of the equation x2 − dy2 = 1, where x and y are unknown positive integers and where d is a known positive integer which is not a perfect square, is ascribed to John Pell. It seems to have been discovered by Fermat, who set it as a challenge problem in 1657. The first European solution is found in a joint work in 1658 by John Wallis and Lord Brouncker; in 1668, a shorter solution was given in an edition of a third mathematician's work by Pell; see ref.


id: list-of-topologies-20260505-0
file: data/en.wikipedia.org/wiki/List_of_topologies-0.md
category: reference
title: List of topologies
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_topologies
date_saved: 2026-05-05T08:17:38.117299+00:00
instance: kb-cron
parent: list-of-topologies-20260505-0
summary:
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property. == Discrete and indiscrete == Discrete topology − All subsets are open. Indiscrete topology, chaotic topology, or Trivial topology − Only the empty set and its complement are open. == Cardinality and ordinals == Cocountable topology Given a topological space ( X , τ ) , {\displaystyle (X,\tau ),} the cocountable extension topology on X {\displaystyle X} is the topology having as a subbasis the union of τ and the family of all subsets of X {\displaystyle X} whose complements in X {\displaystyle X} are countable. Cofinite topology Double-pointed cofinite topology Ordinal number topology Pseudo-arc Ran space Tychonoff plank === Finite spaces === Discrete two-point space − The simplest example of a totally disconnected discrete space. Finite topological space Pseudocircle − A finite topological space on 4 elements that fails to satisfy any separation axiom besides T0. However, from the viewpoint of algebraic topology, it has the remarkable property that it


id: list-of-topologies-20260505-1
file: data/en.wikipedia.org/wiki/List_of_topologies-1.md
category: reference
title: List of topologies
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_topologies
date_saved: 2026-05-05T08:17:38.117299+00:00
instance: kb-cron
parent: list-of-topologies-20260505-0
summary:
Alexandroff plank Appert topology − A Hausdorff, perfectly normal (T6), zero-dimensional space that is countable, but neither first countable, locally compact, nor countably compact. Arens square Bullet-riddled square - The space [ 0 , 1 ] 2 ∖ Q 2 , {\displaystyle [0,1]^{2}\setminus \mathbb {Q} ^{2},} where [ 0 , 1 ] 2 ∩ Q 2 {\displaystyle [0,1]^{2}\cap \mathbb {Q} ^{2}} is the set of bullets. Neither of these sets is Jordan measurable although both are Lebesgue measurable. Cantor tree Comb space Dieudonné plank Double origin topology Dunce hat (topology) Either–or topology Excluded point topology − A topological space where the open sets are defined in terms of the exclusion of a particular point. Fort space Half-disk topology Hilbert cube − [ 0 , 1 / 1 ] × [ 0 , 1 / 2 ] × [ 0 , 1 / 3 ] × ⋯ {\displaystyle [0,1/1]\times [0,1/2]\times [0,1/3]\times \cdots } with the product topology. Infinite broom Integer broom topology K-topology Knaster–Kuratowski fan Long line (topology) Moore plane, also called the Niemytzki plane − A first countable, separable, completely regular, Hausdorff, Moore space that is not normal, Lindelöf, metrizable, second countable, nor locally compact. It also an uncountable closed


id: list-of-topology-topics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_topology_topics-0.md
category: reference
title: List of topology topics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_topology_topics
date_saved: 2026-05-05T08:17:39.346041+00:00
instance: kb-cron
parent: list-of-topology-topics-20260505-0
summary:
In mathematics, topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connectedness, which allows distinguishing a circle from two non-intersecting circles. The ideas underlying topology go back to Gottfried Leibniz, who in the 17th century envisioned the geometria situs and analysis situs. Leonhard Euler's Seven Bridges of Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th century, although it


id: list-of-algebraic-topology-topics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_algebraic_topology_topics-0.md
category: reference
title: List of algebraic topology topics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_algebraic_topology_topics
date_saved: 2026-05-05T08:17:40.558645+00:00
instance: kb-cron
parent: list-of-algebraic-topology-topics-20260505-0
summary:
This is a list of algebraic topology topics. Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. == Homology (mathematics) == Simplex Simplicial complex Polytope Triangulation Barycentric subdivision Simplicial approximation theorem Abstract simplicial complex Simplicial set Simplicial category Chain (algebraic topology) Betti number Euler characteristic Genus Riemann–Hurwitz formula Singular homology Cellular homology Relative homology Mayer–Vietoris sequence Excision theorem Universal coefficient theorem Cohomology List of cohomology theories Cocycle class Cup product Cohomology ring De Rham cohomology Čech cohomology Alexander–Spanier cohomology Intersection cohomology Lusternik–Schnirelmann category Poincaré duality Fundamental class Applications Jordan curve theorem Brouwer fixed point theorem Invariance of domain Lefschetz fixed-point theorem Hairy ball theorem Degree of a continuous mapping Borsuk–Ulam theorem Ham sandwich theorem Homology sphere == Homotopy theory == Homotopy Path (topology) Fundamental group Homotopy group Seifert–van


id: list-of-general-topology-topics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_general_topology_topics-0.md
category: reference
title: List of general topology topics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_general_topology_topics
date_saved: 2026-05-05T08:17:41.721700+00:00
instance: kb-cron
parent: list-of-general-topology-topics-20260505-0
summary:
This is a list of general topology topics. == Basic concepts == Topological space Topological property Open set, closed set Clopen set Closure Boundary Interior Density G-delta set, F-sigma set Closeness Neighborhood Continuity (topology) Homeomorphism Local homeomorphism Open and closed maps Embedding Germ Basis Subbasis Open cover Locally finite space Covering space Atlas == Limits == Limit point Net Filter Ultrafilter == Topological properties == Baire category theorem Nowhere dense Baire space Banach–Mazur game Meagre set Comeagre set === Compactness and countability === Compact space Relatively compact subspace Heine–Borel theorem Tychonoff's theorem Finite intersection property Compactification Measure of non-compactness Paracompact space Locally compact space Compactly generated space Axiom of countability Sequential space First-countable space Second-countable space Separable space Lindelöf space Sigma-compact space === Connectedness === Connected space Simply connected space Path connected space === Separation axioms === T0 space T1 space Hausdorff space Completely Hausdorff space Regular space Tychonoff space Normal space Urysohn's lemma Tietze extension theorem Paracompact Separated sets == Topological constructions == Direct sum and the dual construction product Subspace and the dual construction quotient Topological tensor product == Examples == Discrete space Locally constant function Trivial topology Cofinite topology Cocountable topology Finer topology Product topology Restricted product


id: list-of-geometric-topology-topics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_geometric_topology_topics-0.md
category: reference
title: List of geometric topology topics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_geometric_topology_topics
date_saved: 2026-05-05T08:17:42.922521+00:00
instance: kb-cron
parent: list-of-geometric-topology-topics-20260505-0
summary:
This is a list of geometric topology topics. == Low-dimensional topology == === Knot theory === Knot (mathematics) Link (knot theory) Wild knots Examples of knots (and links) Unknot Trefoil knot Figure-eight knot (mathematics) Borromean rings Types of knots (and links) Torus knot Prime knot Alternating knot Hyperbolic link Knot invariants Crossing number Linking number Skein relation Knot polynomials Alexander polynomial Jones polynomial Knot group Writhe Quandle Seifert surface Braids Braid theory Braid group Kirby calculus === Surfaces === Genus (mathematics) Examples Positive Euler characteristic 2-disk Sphere Real projective plane Zero Euler characteristic Annulus Möbius strip Torus Klein bottle Negative Euler characteristic The boundary of the pretzel is a genus three surface Embedded/Immersed in Euclidean space Cross-cap Boy's surface Roman surface Steiner surface Alexander horned sphere Klein bottle Mapping class group Dehn twist Nielsen–Thurston classification === Three-manifolds === Moise's Theorem (see also Hauptvermutung) Poincaré conjecture Thurston elliptization conjecture Thurston's geometrization conjecture Hyperbolic 3-manifolds Spherical 3-manifolds Euclidean 3-manifolds, Bieberbach Theorem, Flat manifolds, Crystallographic groups Seifert fiber space Heegaard splitting Waldhausen conjecture Compression body Handlebody Incompressible surface Dehn's lemma Loop theorem (aka the Disk theorem) Sphere theorem Haken manifold JSJ decomposition Branched surface Lamination Examples 3-sphere Torus bundles Surface bundles over the


id: list-of-transforms-20260505-0
file: data/en.wikipedia.org/wiki/List_of_transforms-0.md
category: reference
title: List of transforms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_transforms
date_saved: 2026-05-05T08:17:44.168043+00:00
instance: kb-cron
parent: list-of-transforms-20260505-0
summary:
This is a list of transforms in mathematics. == Integral transforms == Abel transform Aboodh transform Bateman transform Fourier transform Fourier cosine transform Fourier sine transform Fractional Fourier transform Short-time Fourier transform Rectangular mask short-time Fourier transform Fourier–Bros–Iagolnitzer transform Gabor transform Hankel transform Hartley transform Hermite transform Hilbert transform Hilbert–Schmidt integral operator Jacobi transform Laguerre transform Laplace transform Inverse Laplace transform Two-sided Laplace transform Inverse two-sided Laplace transform Laplace–Carson transform Laplace–Stieltjes transform Legendre transform Associated Legendre transform Linear canonical transform Mellin transform Inverse Mellin transform Poisson–Mellin–Newton cycle N-transform Radon transform X-ray transform Shehu transform Stieltjes transformation Sumudu transform Wavelet transform (integral) Weierstrass transform == Discrete transforms == Binomial transform Discrete Fourier transform, DFT Fast Fourier transform, a popular implementation of the DFT Discrete cosine transform Modified discrete cosine transform Discrete Hartley transform Discrete sine transform Discrete wavelet transform Hadamard transform (or, Walsh–Hadamard transform) Fast wavelet transform Hankel transform, the determinant of the Hankel matrix Discrete Chebyshev transform Equivalent, up to a diagonal scaling, to a discrete cosine transform Finite Legendre transform Irrational base discrete weighted transform Mojette transform Number-theoretic transform Spherical Harmonic transform Stirling transform == Discrete-time transforms == These transforms have a continuous frequency domain: Discrete-time Fourier transform Z-transform


id: list-of-triangle-inequalities-20260505-0
file: data/en.wikipedia.org/wiki/List_of_triangle_inequalities-0.md
category: reference
title: List of triangle inequalities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_triangle_inequalities
date_saved: 2026-05-05T08:17:45.554884+00:00
instance: kb-cron
parent: list-of-triangle-inequalities-20260505-0
summary:
In geometry, triangle inequalities are inequalities involving the parameters of triangles, that hold for every triangle, or for every triangle meeting certain conditions. The inequalities give an ordering of two different values: they are of the form "less than", "less than or equal to", "greater than", or "greater than or equal to". The parameters in a triangle inequality can be the side lengths, the semiperimeter, the angle measures, the values of trigonometric functions of those angles, the area of the triangle, the medians of the sides, the altitudes, the lengths of the internal angle bisectors from each angle to the opposite side, the perpendicular bisectors of the sides, the distance from an arbitrary point to another point, the inradius, the exradii, the circumradius, and/or other quantities. Unless otherwise specified, this article deals with triangles in the Euclidean plane. == Main parameters and notation == The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c; the semiperimeter s = ⁠a + b + c/2⁠ (half the perimeter p); the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the


id: list-of-triangle-inequalities-20260505-1
file: data/en.wikipedia.org/wiki/List_of_triangle_inequalities-1.md
category: reference
title: List of triangle inequalities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_triangle_inequalities
date_saved: 2026-05-05T08:17:45.554884+00:00
instance: kb-cron
parent: list-of-triangle-inequalities-20260505-0
summary:
each holding with equality only when a = b = c. This says that in the non-equilateral case the harmonic mean of the sides is less than their geometric mean, which in turn is less than their arithmetic mean, and which in turn is less than their quadratic mean. == Angles == cos ⁡ A + cos ⁡ B + cos ⁡ C ≤ 3 2 . {\displaystyle \cos A+\cos B+\cos C\leq {\frac {3}{2}}.} ( 1 − cos ⁡ A ) ( 1 − cos ⁡ B ) ( 1 − cos ⁡ C ) ≥ cos ⁡ A ⋅ cos ⁡ B ⋅ cos ⁡ C . {\displaystyle (1-\cos A)(1-\cos B)(1-\cos C)\geq \cos A\cdot \cos B\cdot \cos C.} cos 4 ⁡ A 2 + cos 4 ⁡ B 2 + cos 4 ⁡ C 2 ≤ s 3 2 a b c {\displaystyle \cos ^{4}{\frac {A}{2}}+\cos ^{4}{\frac {B}{2}}+\cos ^{4}{\frac {C}{2}}\leq {\frac {s^{3}}{2abc}}} for semi-perimeter s, with equality only in the equilateral case. a + b + c ≥ 2 b c cos ⁡ A + 2 c a cos ⁡ B + 2 a b cos ⁡ C . {\displaystyle a+b+c\geq 2{\sqrt {bc}}\cos A+2{\sqrt {ca}}\cos B+2{\sqrt {ab}}\cos C.} sin


id: list-of-triangle-inequalities-20260505-2
file: data/en.wikipedia.org/wiki/List_of_triangle_inequalities-2.md
category: reference
title: List of triangle inequalities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_triangle_inequalities
date_saved: 2026-05-05T08:17:45.554884+00:00
instance: kb-cron
parent: list-of-triangle-inequalities-20260505-0
summary:
a b + b c + c a ≥ 4 3 ⋅ T {\displaystyle ab+bc+ca\geq 4{\sqrt {3}}\cdot T} and T ≤ a b c 2 a + b + c a 3 + b 3 + c 3 + a b c ≤ 1 4 3 ( a + b + c ) 3 ( a b c ) 4 a 3 + b 3 + c 3 6 ≤ 3 4 ( a b c ) 2 3 . {\displaystyle T\leq {\frac {abc}{2}}{\sqrt {\frac {a+b+c}{a^{3}+b^{3}+c^{3}+abc}}}\leq {\frac {1}{4}}{\sqrt[{6}]{\frac {3(a+b+c)^{3}(abc)^{4}}{a^{3}+b^{3}+c^{3}}}}\leq {\frac {\sqrt {3}}{4}}(abc)^{\frac {2}{3}}.} From the rightmost upper bound on T, using the arithmetic-geometric mean inequality, is obtained the isoperimetric inequality for triangles: T ≤ 3 36 ( a + b + c ) 2 = 3 9 s 2 {\displaystyle T\leq {\frac {\sqrt {3}}{36}}(a+b+c)^{2}={\frac {\sqrt {3}}{9}}s^{2}} for semiperimeter s. This is sometimes stated in terms of perimeter p as p 2 ≥ 12 3 ⋅ T , {\displaystyle p^{2}\geq 12{\sqrt {3}}\cdot T,} with equality for the equilateral triangle. This is strengthened by T ≤ 3 4 ( a b c ) 2 3 . {\displaystyle T\leq {\frac {\sqrt {3}}{4}}\left(abc\right)^{\frac {2}{3}}.} Bonnesen's inequality also strengthens the isoperimetric inequality: π 2 (


id: list-of-triangle-inequalities-20260505-3
file: data/en.wikipedia.org/wiki/List_of_triangle_inequalities-3.md
category: reference
title: List of triangle inequalities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_triangle_inequalities
date_saved: 2026-05-05T08:17:45.554884+00:00
instance: kb-cron
parent: list-of-triangle-inequalities-20260505-0
summary:
== Altitudes == The altitudes ha, etc. each connect a vertex to the opposite side and are perpendicular to that side. They satisfy both h a + h b + h c ≤ 3 2 ( a + b + c ) {\displaystyle h_{a}+h_{b}+h_{c}\leq {\frac {\sqrt {3}}{2}}(a+b+c)} and h a 2 + h b 2 + h c 2 ≤ 3 4 ( a 2 + b 2 + c 2 ) . {\displaystyle h_{a}^{2}+h_{b}^{2}+h_{c}^{2}\leq {\frac {3}{4}}(a^{2}+b^{2}+c^{2}).} In addition, if a ≥ b ≥ c , {\displaystyle a\geq b\geq c,} then a + h a ≥ b + h b ≥ c + h c . {\displaystyle a+h_{a}\geq b+h_{b}\geq c+h_{c}.} We also have h a 2 ( b 2 + c 2 ) ⋅ h b 2 ( c 2 + a 2 ) ⋅ h c 2 ( a 2 + b 2 ) ≤ ( 3 8 ) 3 . {\displaystyle {\frac {h_{a}^{2}}{(b^{2}+c^{2})}}\cdot {\frac {h_{b}^{2}}{(c^{2}+a^{2})}}\cdot {\frac {h_{c}^{2}}{(a^{2}+b^{2})}}\leq \left({\frac {3}{8}}\right)^{3}.} For internal angle bisectors ta, tb, tc from vertices A, B, C and circumcenter R and incenter r, we have h a t a + h b t b + h c t c ≥ R + 4 r


id: list-of-triangle-inequalities-20260505-4
file: data/en.wikipedia.org/wiki/List_of_triangle_inequalities-4.md
category: reference
title: List of triangle inequalities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_triangle_inequalities
date_saved: 2026-05-05T08:17:45.554884+00:00
instance: kb-cron
parent: list-of-triangle-inequalities-20260505-0
summary:
2 ( P A + P B + P C ) > A B + B C + C A > P A + P B + P C , {\displaystyle 2(PA+PB+PC)>AB+BC+CA>PA+PB+PC,} and more strongly than the second of these inequalities is: If A B {\displaystyle AB} is the shortest side of the triangle, then P A + P B + P C ≤ A C + B C . {\displaystyle PA+PB+PC\leq AC+BC.} We also have Ptolemy's inequality P A ⋅ B C + P B ⋅ C A > P C ⋅ A B {\displaystyle PA\cdot BC+PB\cdot CA>PC\cdot AB} for interior point P and likewise for cyclic permutations of the vertices. If we draw perpendiculars from interior point P to the sides of the triangle, intersecting the sides at D, E, and F, we have P A ⋅ P B ⋅ P C ≥ ( P D + P E ) ( P E + P F ) ( P F + P D ) . {\displaystyle PA\cdot PB\cdot PC\geq (PD+PE)(PE+PF)(PF+PD).} Further, the Erdős–Mordell inequality states that P A + P B + P C P D + P E + P F ≥ 2 {\displaystyle {\frac {PA+PB+PC}{PD+PE+PF}}\geq 2}


id: list-of-triangle-inequalities-20260505-5
file: data/en.wikipedia.org/wiki/List_of_triangle_inequalities-5.md
category: reference
title: List of triangle inequalities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_triangle_inequalities
date_saved: 2026-05-05T08:17:45.554884+00:00
instance: kb-cron
parent: list-of-triangle-inequalities-20260505-0
summary:
P A 4 + P B 4 + P C 4 + k ( P A ⋅ P B ⋅ P C ) 4 3 ≥ 16 ( k + 3 ) r 4 {\displaystyle PA^{4}+PB^{4}+PC^{4}+k(PA\cdot PB\cdot PC)^{\frac {4}{3}}\geq 16(k+3)r^{4}} for k = 0, 1, ..., 9. Furthermore, for circumradius R, ( P A ⋅ P B ) 3 2 + ( P B ⋅ P C ) 3 2 + ( P C ⋅ P A ) 3 2 ≥ 12 R r 2 ; {\displaystyle \left(PA\cdot PB\right)^{\frac {3}{2}}+\left(PB\cdot PC\right)^{\frac {3}{2}}+\left(PC\cdot PA\right)^{\frac {3}{2}}\geq 12Rr^{2};} ( P A ⋅ P B ) 2 + ( P B ⋅ P C ) 2 + ( P C ⋅ P A ) 2 ≥ 8 ( R + r ) R r 2 ; {\displaystyle (PA\cdot PB)^{2}+(PB\cdot PC)^{2}+(PC\cdot PA)^{2}\geq 8(R+r)Rr^{2};} ( P A ⋅ P B ) 2 + ( P B ⋅ P C ) 2 + ( P C ⋅ P A ) 2 ≥ 48 r 4 ; {\displaystyle (PA\cdot PB)^{2}+(PB\cdot PC)^{2}+(PC\cdot PA)^{2}\geq 48r^{4};} ( P A ⋅ P B ) 2 + ( P B ⋅ P C ) 2 + ( P C ⋅ P A )


id: list-of-triangle-inequalities-20260505-6
file: data/en.wikipedia.org/wiki/List_of_triangle_inequalities-6.md
category: reference
title: List of triangle inequalities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_triangle_inequalities
date_saved: 2026-05-05T08:17:45.554884+00:00
instance: kb-cron
parent: list-of-triangle-inequalities-20260505-0
summary:
s ≤ ( 3 3 − 4 ) r + 2 R . {\displaystyle s\leq (3{\sqrt {3}}-4)r+2R.} We also have, for all acute triangles, s > 2 R + r . {\displaystyle s>2R+r.} For incircle center I, let AI, BI, and CI extend beyond I to intersect the circumcircle at D, E, and F respectively. Then A I I D + B I I E + C I I F ≥ 3. {\displaystyle {\frac {AI}{ID}}+{\frac {BI}{IE}}+{\frac {CI}{IF}}\geq 3.} In terms of the vertex angles we have cos ⁡ A ⋅ cos ⁡ B ⋅ cos ⁡ C ≤ ( r R 2 ) 2 . {\displaystyle \cos A\cdot \cos B\cdot \cos C\leq \left({\frac {r}{R{\sqrt {2}}}}\right)^{2}.} Denote as R A , R B , R C {\displaystyle R_{A},R_{B},R_{C}} the tanradii of the triangle. Then 4 R ≤ 1 R A + 1 R B + 1 R C ≤ 2 r {\displaystyle {\frac {4}{R}}\leq {\frac {1}{R_{A}}}+{\frac {1}{R_{B}}}+{\frac {1}{R_{C}}}\leq {\frac {2}{r}}} with equality only in the equilateral case, and 9 2 r ≤ R A + R B + R C ≤ 2 R + 1 2 r {\displaystyle {\frac {9}{2}}r\leq R_{A}+R_{B}+R_{C}\leq 2R+{\frac {1}{2}}r} with equality only in the equilateral case. ===


id: list-of-triangle-inequalities-20260505-7
file: data/en.wikipedia.org/wiki/List_of_triangle_inequalities-7.md
category: reference
title: List of triangle inequalities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_triangle_inequalities
date_saved: 2026-05-05T08:17:45.554884+00:00
instance: kb-cron
parent: list-of-triangle-inequalities-20260505-0
summary:
=== Inscribed triangle === If three points D, E, F on the respective sides AB, BC, and CA of a reference triangle ABC are the vertices of an inscribed triangle, which thereby partitions the reference triangle into four triangles, then the area of the inscribed triangle is greater than the area of at least one of the other interior triangles, unless the vertices of the inscribed triangle are at the midpoints of the sides of the reference triangle (in which case the inscribed triangle is the medial triangle and all four interior triangles have equal areas): Area(DEF) ≥ min ( Area(BED), Area(CFE), Area(ADF) ) . {\displaystyle {\text{Area(DEF)}}\geq \min({\text{Area(BED), Area(CFE), Area(ADF)}}).} === Inscribed squares === An acute triangle has three inscribed squares, each with one side coinciding with part of a side of the triangle and with the square's other two vertices on the remaining two sides of the triangle. (A right triangle has only two distinct inscribed squares.) If one of these squares has side length xa and another has side length xb with xa < xb, then 1 ≥ x a x b ≥ 2 2 3 ≈ 0.94. {\displaystyle 1\geq {\frac {x_{a}}{x_{b}}}\geq {\frac {2{\sqrt {2}}}{3}}\approx 0.94.} Moreover, for


id: list-of-trigonometric-identities-20260505-0
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-0.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity. == Pythagorean identities == The basic relationship between the sine and cosine is given by the Pythagorean identity: sin 2 ⁡ θ + cos 2 ⁡ θ = 1 , {\displaystyle \sin ^{2}\theta +\cos ^{2}\theta =1,} where sin 2 ⁡ θ {\displaystyle \sin ^{2}\theta } means ( sin ⁡ θ ) 2 {\displaystyle {(\sin \theta )}^{2}} and cos 2 ⁡ θ {\displaystyle \cos ^{2}\theta } means ( cos ⁡ θ ) 2 . {\displaystyle {(\cos \theta )}^{2}.} This can be viewed as a version of the Pythagorean theorem, and follows from


id: list-of-trigonometric-identities-20260505-1
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-1.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
== Angle sum and difference identities == These are also known as the angle addition and subtraction theorems (or formulae). sin ⁡ ( α + β ) = sin ⁡ α cos ⁡ β + cos ⁡ α sin ⁡ β sin ⁡ ( α − β ) = sin ⁡ α cos ⁡ β − cos ⁡ α sin ⁡ β cos ⁡ ( α + β ) = cos ⁡ α cos ⁡ β − sin ⁡ α sin ⁡ β cos ⁡ ( α − β ) = cos ⁡ α cos ⁡ β + sin ⁡ α sin ⁡ β {\displaystyle {\begin{aligned}\sin(\alpha +\beta )&=\sin \alpha \cos \beta +\cos \alpha \sin \beta \\\sin(\alpha -\beta )&=\sin \alpha \cos \beta -\cos \alpha \sin \beta \\\cos(\alpha +\beta )&=\cos \alpha \cos \beta -\sin \alpha \sin \beta \\\cos(\alpha -\beta )&=\cos \alpha \cos \beta +\sin \alpha \sin \beta \end{aligned}}} The angle difference identities for sin ⁡ ( α − β ) {\displaystyle \sin(\alpha -\beta )} and cos ⁡ ( α − β ) {\displaystyle \cos(\alpha -\beta )} can be derived from the angle sum versions (and vice versa) by substituting − β {\displaystyle -\beta } for β {\displaystyle \beta } and using the


id: list-of-trigonometric-identities-20260505-2
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-2.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
tan ⁡ ( ∑ i θ i ) = sin ( ∑ i θ i ) / ∏ i cos ⁡ θ i cos ( ∑ i θ i ) / ∏ i cos ⁡ θ i = ∑ odd k ≥ 1 ( − 1 ) k − 1 2 ∑ A ⊆ { 1 , 2 , 3 , … } | A | = k ∏ i ∈ A tan ⁡ θ i ∑ even k ≥ 0 ( − 1 ) k 2 ∑ A ⊆ { 1 , 2 , 3 , … } | A | = k ∏ i ∈ A tan ⁡ θ i = e 1 − e 3 + e 5 − ⋯ e 0 − e 2 + e 4 − ⋯ cot ⁡ ( ∑ i θ i ) = e 0 − e 2 + e 4 − ⋯ e 1 − e 3 + e 5 − ⋯ {\displaystyle {\begin{aligned}\tan {\Bigl (}\sum _{i}\theta _{i}{\Bigr )}&={\frac {{\sin }{\bigl (}\sum _{i}\theta _{i}{\bigr )}/\prod _{i}\cos \theta _{i}}{{\cos }{\bigl (}\sum _{i}\theta _{i}{\bigr )}/\prod _{i}\cos \theta _{i}}}\\[10pt]&={\frac {\displaystyle \sum _{{\text{odd}}\ k\geq 1}(-1)^{\frac {k-1}{2}}\sum _{\begin{smallmatrix}A\subseteq \{1,2,3,\dots \}\\\left|A\right|=k\end{smallmatrix}}\prod _{i\in A}\tan \theta _{i}}{\displaystyle \sum


id: list-of-trigonometric-identities-20260505-3
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-3.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
sec ⁡ ( α + β + γ ) = sec ⁡ α sec ⁡ β sec ⁡ γ 1 − tan ⁡ α tan ⁡ β − tan ⁡ α tan ⁡ γ − tan ⁡ β tan ⁡ γ csc ⁡ ( α + β + γ ) = sec ⁡ α sec ⁡ β sec ⁡ γ tan ⁡ α + tan ⁡ β + tan ⁡ γ − tan ⁡ α tan ⁡ β tan ⁡ γ . {\displaystyle {\begin{aligned}\sec(\alpha +\beta +\gamma )&={\frac {\sec \alpha \sec \beta \sec \gamma }{1-\tan \alpha \tan \beta -\tan \alpha \tan \gamma -\tan \beta \tan \gamma }}\\[8pt]\csc(\alpha +\beta +\gamma )&={\frac {\sec \alpha \sec \beta \sec \gamma }{\tan \alpha +\tan \beta +\tan \gamma -\tan \alpha \tan \beta \tan \gamma }}.\end{aligned}}} === Ptolemy's theorem === Ptolemy's theorem is important in the history of trigonometric identities, as it is how results equivalent to the sum and difference formulas for sine and cosine were first proved. It states that in a cyclic quadrilateral A B C D {\displaystyle ABCD} , as shown in the accompanying figure, the sum of the products of the lengths of opposite sides is equal to the product of the lengths


id: list-of-trigonometric-identities-20260505-4
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-4.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
sin ⁡ ( 3 θ ) = 3 sin ⁡ θ − 4 sin 3 ⁡ θ = 4 sin ⁡ θ sin ⁡ ( π 3 − θ ) sin ⁡ ( π 3 + θ ) cos ⁡ ( 3 θ ) = 4 cos 3 ⁡ θ − 3 cos ⁡ θ = 4 cos ⁡ θ cos ⁡ ( π 3 − θ ) cos ⁡ ( π 3 + θ ) tan ⁡ ( 3 θ ) = 3 tan ⁡ θ − tan 3 ⁡ θ 1 − 3 tan 2 ⁡ θ = tan ⁡ θ tan ⁡ ( π 3 − θ ) tan ⁡ ( π 3 + θ ) cot ⁡ ( 3 θ ) = 3 cot ⁡ θ − cot 3 ⁡ θ 1 − 3 cot 2 ⁡ θ sec ⁡ ( 3 θ ) = sec 3 ⁡ θ 4 − 3 sec 2 ⁡ θ csc ⁡ ( 3 θ ) = csc 3 ⁡ θ 3 csc 2 ⁡ θ − 4 {\displaystyle {\begin{aligned}\sin(3\theta )&=3\sin \theta -4\sin ^{3}\theta &&=4\sin \theta \sin \left({\tfrac {\pi }{3}}-\theta \right)\sin \left({\tfrac {\pi }{3}}+\theta \right)\\\cos(3\theta )&=4\cos ^{3}\theta -3\cos \theta &&=4\cos


id: list-of-trigonometric-identities-20260505-5
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-5.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
cos ⁡ ( ( n − 1 ) x + x ) = cos ⁡ ( ( n − 1 ) x ) cos ⁡ x − sin ⁡ ( ( n − 1 ) x ) sin ⁡ x cos ⁡ ( ( n − 1 ) x − x ) = cos ⁡ ( ( n − 1 ) x ) cos ⁡ x + sin ⁡ ( ( n − 1 ) x ) sin ⁡ x {\displaystyle {\begin{aligned}\cos {\bigl (}(n-1)x+x{\bigr )}&=\cos {\bigl (}(n-1)x{\bigr )}\cos x-\sin {\bigl (}(n-1)x{\bigr )}\sin x\\\cos {\bigl (}(n-1)x-x{\bigr )}&=\cos {\bigl (}(n-1)x{\bigr )}\cos x+\sin {\bigl (}(n-1)x{\bigr )}\sin x\end{aligned}}} It follows by induction that cos ⁡ ( n x ) {\displaystyle \cos(nx)} is a polynomial of cos ⁡ x , {\displaystyle \cos x,} the so-called Chebyshev polynomial of the first kind, see Chebyshev polynomials#Trigonometric definition. Similarly, sin ⁡ ( n x ) {\displaystyle \sin(nx)} can be computed from sin ⁡ ( ( n − 1 ) x ) , {\displaystyle \sin((n-1)x),} sin ⁡ ( ( n − 2 ) x ) , {\displaystyle \sin((n-2)x),} and cos ⁡ x {\displaystyle \cos x} with sin ⁡ ( n x ) = 2 cos ⁡ x sin ⁡


id: list-of-trigonometric-identities-20260505-6
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-6.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
The product-to-sum identities or prosthaphaeresis formulae can be proven by expanding their right-hand sides using the angle addition theorems. Historically, the first four of these were known as Werner's formulas, after Johannes Werner who used them for astronomical calculations. See amplitude modulation for an application of the product-to-sum formulae, and beat (acoustics) and phase detector for applications of the sum-to-product formulae. === Product-to-sum identities === The product of two sines or cosines of different angles can be converted to a sum of trigonometric functions of a sum and difference of those angles: cos ⁡ θ cos ⁡ φ = 1 2 ( cos ⁡ ( θ − φ ) + cos ⁡ ( θ + φ ) ) , sin ⁡ θ sin ⁡ φ = 1 2 ( cos ⁡ ( θ − φ ) − cos ⁡ ( θ + φ ) ) , sin ⁡ θ cos ⁡ φ = 1 2 ( sin ⁡ ( θ + φ ) + sin ⁡ ( θ − φ ) ) , cos ⁡ θ sin ⁡ φ = 1 2 ( sin ⁡ ( θ + φ ) − sin ⁡ ( θ − φ ) ) .


id: list-of-trigonometric-identities-20260505-7
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-7.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
cot ⁡ ( z − a 1 ) cot ⁡ ( z − a 2 ) = − 1 + cot ⁡ ( a 1 − a 2 ) cot ⁡ ( z − a 1 ) + cot ⁡ ( a 2 − a 1 ) cot ⁡ ( z − a 2 ) . {\displaystyle \cot(z-a_{1})\cot(z-a_{2})=-1+\cot(a_{1}-a_{2})\cot(z-a_{1})+\cot(a_{2}-a_{1})\cot(z-a_{2}).} === Finite products of trigonometric functions === For coprime integers n, m ∏ k = 1 n ( 2 a + 2 cos ⁡ ( 2 π k m n + x ) ) = 2 ( T n ( a ) + ( − 1 ) n + m cos ⁡ ( n x ) ) {\displaystyle \prod _{k=1}^{n}\left(2a+2\cos \left({\frac {2\pi km}{n}}+x\right)\right)=2\left(T_{n}(a)+{(-1)}^{n+m}\cos(nx)\right)} where Tn is the Chebyshev polynomial. The following relationship holds for the sine function ∏ k = 1 n − 1 sin ⁡ ( k π n ) = n 2 n − 1 . {\displaystyle \prod _{k=1}^{n-1}\sin \left({\frac {k\pi }{n}}\right)={\frac {n}{2^{n-1}}}.} More generally for an integer n > 0 sin ⁡ ( n x ) = 2 n − 1 ∏ k = 0 n − 1 sin ⁡ ( k π n + x ) = 2


id: list-of-trigonometric-identities-20260505-8
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-8.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
sin ⁡ ( A + B ) − sin ⁡ ( A − B ) = 2 cos ⁡ A sin ⁡ B . {\displaystyle \sin(A+B)-\sin(A-B)=2\cos A\sin B.} Then let's examine the following formula, 2 sin ⁡ α ∑ k = 1 n cos ⁡ ( 2 k − 1 ) α = 2 sin ⁡ α cos ⁡ α + 2 sin ⁡ α cos ⁡ 3 α + 2 sin ⁡ α cos ⁡ 5 α + ⋯ + 2 sin ⁡ α cos ⁡ ( 2 n − 1 ) α {\displaystyle 2\sin \alpha \sum _{k=1}^{n}\cos(2k-1)\alpha =2\sin \alpha \cos \alpha +2\sin \alpha \cos 3\alpha +2\sin \alpha \cos 5\alpha +\cdots +2\sin \alpha \cos(2n-1)\alpha } and this formula can be written by using the above identity, 2 sin ⁡ α ∑ k = 1 n cos ⁡ ( 2 k − 1 ) α = ∑ k = 1 n ( sin ⁡ ( 2 k α ) − sin ⁡ ( 2 ( k − 1 ) α ) ) = ( sin ⁡ 2 α − sin ⁡ 0 ) + ( sin ⁡ 4 α − sin ⁡ 2 α ) + ( sin ⁡ 6


id: list-of-trigonometric-identities-20260505-9
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-9.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
sin ⁡ x = x ∏ n = 1 ∞ ( 1 − x 2 π 2 n 2 ) , cos ⁡ x = ∏ n = 1 ∞ ( 1 − x 2 π 2 ( n − 1 2 ) ) 2 ) , sinh ⁡ x = x ∏ n = 1 ∞ ( 1 + x 2 π 2 n 2 ) , cosh ⁡ x = ∏ n = 1 ∞ ( 1 + x 2 π 2 ( n − 1 2 ) ) 2 ) . {\displaystyle {\begin{aligned}\sin x&=x\prod _{n=1}^{\infty }\left(1-{\frac {x^{2}}{\pi ^{2}n^{2}}}\right),&\cos x&=\prod _{n=1}^{\infty }\left(1-{\frac {x^{2}}{\pi ^{2}\left(n-{\frac {1}{2}}\right)\!{\vphantom {)}}^{2}}}\right),\\[10mu]\sinh x&=x\prod _{n=1}^{\infty }\left(1+{\frac {x^{2}}{\pi ^{2}n^{2}}}\right),&\cosh x&=\prod _{n=1}^{\infty }\left(1+{\frac {x^{2}}{\pi ^{2}\left(n-{\frac {1}{2}}\right)\!{\vphantom {)}}^{2}}}\right).\end{aligned}}} == Inverse trigonometric functions == The following identities give the result of composing a trigonometric function with an inverse trigonometric function. sin ⁡ ( arcsin ⁡ x ) = x cos ⁡ ( arcsin ⁡ x ) = 1 − x 2 tan ⁡ ( arcsin ⁡ x ) = x 1 − x 2 sin ⁡ ( arccos ⁡ x ) = 1 − x 2 cos ⁡ ( arccos ⁡ x ) = x tan ⁡ ( arccos


id: list-of-trigonometric-identities-20260505-10
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-10.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
arctan ⁡ 1 p = arctan ⁡ 1 p + q + arctan ⁡ q p 2 + p q + 1 . {\displaystyle \arctan {\frac {1}{p}}=\arctan {\frac {1}{p+q}}+\arctan {\frac {q}{p^{2}+pq+1}}.} The curious identity known as Morrie's law, cos ⁡ 20 ∘ ⋅ cos ⁡ 40 ∘ ⋅ cos ⁡ 80 ∘ = 1 8 , {\displaystyle \cos 20^{\circ }\cdot \cos 40^{\circ }\cdot \cos 80^{\circ }={\frac {1}{8}},} is a special case of an identity that contains one variable: ∏ j = 0 k − 1 cos ⁡ ( 2 j x ) = sin ⁡ ( 2 k x ) 2 k sin ⁡ x . {\displaystyle \prod _{j=0}^{k-1}\cos \left(2^{j}x\right)={\frac {\sin \left(2^{k}x\right)}{2^{k}\sin x}}.} Similarly, sin ⁡ 20 ∘ ⋅ sin ⁡ 40 ∘ ⋅ sin ⁡ 80 ∘ = 3 8 {\displaystyle \sin 20^{\circ }\cdot \sin 40^{\circ }\cdot \sin 80^{\circ }={\frac {\sqrt {3}}{8}}} is a special case of an identity with x = 20 ∘ {\displaystyle x=20^{\circ }} : sin ⁡ x ⋅ sin ⁡ ( 60 ∘ − x ) ⋅ sin ⁡ ( 60 ∘ + x ) = sin ⁡ 3 x 4 . {\displaystyle \sin x\cdot \sin \left(60^{\circ }-x\right)\cdot \sin \left(60^{\circ }+x\right)={\frac {\sin 3x}{4}}.} For the


id: list-of-trigonometric-identities-20260505-11
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-11.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
If n is an odd number ( n = 2 m + 1 {\displaystyle n=2m+1} ) we can make use of the symmetries to get ∏ k = 1 m tan ⁡ k π 2 m + 1 = 2 m + 1 {\displaystyle \prod _{k=1}^{m}\tan {\frac {k\pi }{2m+1}}={\sqrt {2m+1}}} The transfer function of the Butterworth low pass filter can be expressed in terms of polynomial and poles. By setting the frequency as the cutoff frequency, the following identity can be proved: ∏ k = 1 n sin ⁡ ( 2 k − 1 ) π 4 n = ∏ k = 1 n cos ⁡ ( 2 k − 1 ) π 4 n = 2 2 n {\displaystyle \prod _{k=1}^{n}\sin {\frac {\left(2k-1\right)\pi }{4n}}=\prod _{k=1}^{n}\cos {\frac {\left(2k-1\right)\pi }{4n}}={\frac {\sqrt {2}}{2^{n}}}} === Computing π === An efficient way to compute π to a large number of digits is based on the following identity without variables, due to Machin. This is known as a Machin-like formula: π 4 = 4 arctan ⁡ 1 5 − arctan ⁡ 1 239 {\displaystyle {\frac {\pi }{4}}=4\arctan {\frac {1}{5}}-\arctan {\frac {1}{239}}} or, alternatively, by using an identity of Leonhard Euler: π 4 = 5 arctan


id: list-of-trigonometric-identities-20260505-12
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-12.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
== Further "conditional" identities for the case α + β + γ = 180° == A conditional trigonometric identity is a trigonometric identity that holds if specified conditions on the arguments to the trigonometric functions are satisfied. The following formulae apply to arbitrary plane triangles and follow from α + β + γ = 180 ∘ , {\displaystyle \alpha +\beta +\gamma =180^{\circ },} as long as the functions occurring in the formulae are well-defined (the latter applies only to the formulae in which tangents and cotangents occur). tan ⁡ α + tan ⁡ β + tan ⁡ γ = tan ⁡ α tan ⁡ β tan ⁡ γ 1 = cot ⁡ β cot ⁡ γ + cot ⁡ γ cot ⁡ α + cot ⁡ α cot ⁡ β cot ⁡ ( α 2 ) + cot ⁡ ( β 2 ) + cot ⁡ ( γ 2 ) = cot ⁡ ( α 2 ) cot ⁡ ( β 2 ) cot ⁡ ( γ 2 ) 1 = tan ⁡ ( β 2 ) tan ⁡ ( γ 2 ) + tan ⁡ ( γ 2 ) tan ⁡ ( α 2 ) + tan ⁡ (


id: list-of-trigonometric-identities-20260505-13
file: data/en.wikipedia.org/wiki/List_of_trigonometric_identities-13.md
category: reference
title: List of trigonometric identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_trigonometric_identities
date_saved: 2026-05-05T08:17:46.795425+00:00
instance: kb-cron
parent: list-of-trigonometric-identities-20260505-0
summary:
=== Dirichlet kernel === The Dirichlet kernel Dn(x) is the function occurring on both sides of the next identity: 1 + 2 cos ⁡ x + 2 cos ⁡ ( 2 x ) + 2 cos ⁡ ( 3 x ) + ⋯ + 2 cos ⁡ ( n x ) = sin ⁡ ( ( n + 1 2 ) x ) sin ⁡ ( 1 2 x ) . {\displaystyle 1+2\cos x+2\cos(2x)+2\cos(3x)+\cdots +2\cos(nx)={\frac {\sin \left(\left(n+{\frac {1}{2}}\right)x\right)}{\sin \left({\frac {1}{2}}x\right)}}.} The convolution of any integrable function of period 2 π {\displaystyle 2\pi } with the Dirichlet kernel coincides with the function's n {\displaystyle n} th-degree Fourier approximation. The same holds for any measure or generalized function. === Tangent half-angle substitution === If we set t = tan ⁡ x 2 , {\displaystyle t=\tan {\frac {x}{2}},} then sin ⁡ x = 2 t 1 + t 2 ; cos ⁡ x = 1 − t 2 1 + t 2 ; e i x = 1 + i t 1 − i t ; d x = 2 d t 1 + t 2 , {\displaystyle \sin x={\frac {2t}{1+t^{2}}};\qquad \cos x={\frac {1-t^{2}}{1+t^{2}}};\qquad e^{ix}={\frac {1+it}{1-it}};\qquad dx={\frac {2\,dt}{1+t^{2}}},} where e i x =


id: outline-of-trigonometry-20260505-0
file: data/en.wikipedia.org/wiki/Outline_of_trigonometry-0.md
category: reference
title: Outline of trigonometry
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Outline_of_trigonometry
date_saved: 2026-05-05T08:17:48.718303+00:00
instance: kb-cron
parent: outline-of-trigonometry-20260505-0
summary:
The following outline is provided as an overview of and topical guide to trigonometry: Trigonometry – branch of mathematics that studies the relationships between the sides and the angles in triangles. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. == Basics == Geometry – mathematics concerned with questions of shape, size, the relative position of figures, and the properties of space. Geometry is used extensively in trigonometry. Angle – the angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Ratio – a ratio indicates how many times one number contains another == Content of trigonometry == Trigonometry Trigonometric functions Trigonometric identities Euler's formula == Scholars == Archimedes Aristarchus Aryabhata Bhaskara I Claudius Ptolemy Euclid Hipparchus Madhava of Sangamagrama Ptolemy Pythagoras Regiomontanus == History == Aristarchus's inequality Bhaskara I's sine approximation formula Greek astronomy Indian astronomy Jyā, koti-jyā and utkrama-jyā Madhava's sine table Ptolemy's table of chords Rule of marteloio Āryabhaṭa's sine table == Fields ==


id: list-of-undecidable-problems-20260505-0
file: data/en.wikipedia.org/wiki/List_of_undecidable_problems-0.md
category: reference
title: List of undecidable problems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_undecidable_problems
date_saved: 2026-05-05T08:17:51.782326+00:00
instance: kb-cron
parent: list-of-undecidable-problems-20260505-0
summary:
In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist. More formally, an undecidable problem is a problem whose language is not a recursive set; see the article Decidable language. There are uncountably many undecidable problems, so the list below is necessarily incomplete. Though undecidable languages are not recursive languages, they may be subsets of Turing recognizable languages: i.e., such undecidable languages may be recursively enumerable. Many, if not most, undecidable problems in mathematics can be posed as word problems: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of statements undecidable in ZFC. == Problems about abstract machines == The halting problem (determining whether a Turing machine halts on a given input) and the mortality problem (determining whether it halts for every starting configuration). Determining whether a Turing machine is a busy beaver champion (i.e., is the longest-running among halting Turing machines with the same number of states and symbols). Rice's theorem states that for all nontrivial properties of partial functions, it is undecidable whether a given machine


id: list-of-undecidable-problems-20260505-1
file: data/en.wikipedia.org/wiki/List_of_undecidable_problems-1.md
category: reference
title: List of undecidable problems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_undecidable_problems
date_saved: 2026-05-05T08:17:51.782326+00:00
instance: kb-cron
parent: list-of-undecidable-problems-20260505-0
summary:
== Other problems == The problem of determining if a given set of Wang tiles can tile the plane. The problem of determining if a given set of polyominoes can tile the plane. The problem of determining the Kolmogorov complexity of a string. Determining whether a given initial point with rational coordinates is periodic, or whether it lies in the basin of attraction of a given open set, in a piecewise-linear iterated map in two dimensions, or in a piecewise-linear flow in three dimensions. Finding the capacity of an information-stable finite state machine channel. In network coding, determining whether a network is solvable. Determining whether a player has a winning strategy in a game of Magic: The Gathering. Planning in a partially observable Markov decision process. Planning air travel from one destination to another, when fares are taken into account. == See also == Lists of problems List of unsolved problems Reduction (complexity) Unknowability == Notes == == Bibliography == Brookshear, J. Glenn (1989). Theory of Computation: Formal Languages, Automata, and Complexity. Redwood City, California: Benjamin/Cummings Publishing Company, Inc. Appendix C includes impossibility of algorithms deciding if a grammar contains ambiguities, and impossibility of verifying program correctness by an algorithm


id: list-of-statements-independent-of-zfc-20260505-0
file: data/en.wikipedia.org/wiki/List_of_statements_independent_of_ZFC-0.md
category: reference
title: List of statements independent of ZFC
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_statements_independent_of_ZFC
date_saved: 2026-05-05T08:17:53.109673+00:00
instance: kb-cron
parent: list-of-statements-independent-of-zfc-20260505-0
summary:
The mathematical statements discussed below are provably independent of ZFC (the canonical axiomatic set theory of contemporary mathematics, consisting of the Zermelo–Fraenkel axioms plus the axiom of choice), assuming that ZFC is consistent. A statement is independent of ZFC (sometimes phrased "undecidable in ZFC") if it can neither be proven nor disproven from the axioms of ZFC. == Axiomatic set theory == In 1931, Kurt Gödel proved his incompleteness theorems, establishing that many mathematical theories, including ZFC, cannot prove their own consistency. Assuming ω-consistency of such a theory, the consistency statement can also not be disproven, meaning it is independent. A few years later, other arithmetic statements were defined that are independent of any such theory, see for example Rosser's trick. The following set theoretic statements are independent of ZFC, among others: the continuum hypothesis or CH (Gödel produced a model of ZFC in which CH is true, showing that CH cannot be disproven in ZFC; Paul Cohen later invented the method of forcing to exhibit a model of ZFC in which CH fails, showing that CH cannot be proven in ZFC. The following four independence results are also due to Gödel/Cohen.); the generalized continuum hypothesis (GCH); a related independent


id: list-of-statements-independent-of-zfc-20260505-1
file: data/en.wikipedia.org/wiki/List_of_statements_independent_of_ZFC-1.md
category: reference
title: List of statements independent of ZFC
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_statements_independent_of_ZFC
date_saved: 2026-05-05T08:17:53.109673+00:00
instance: kb-cron
parent: list-of-statements-independent-of-zfc-20260505-0
summary:
One can write down a concrete polynomial p ∈ Z[x1, ..., x9] such that the statement "there are integers m1, ..., m9 with p(m1, ..., m9) = 0" can neither be proven nor disproven in ZFC (assuming ZFC is consistent). This follows from Yuri Matiyasevich's resolution of Hilbert's tenth problem; the polynomial is constructed so that it has an integer root if and only if ZFC is inconsistent. == Measure theory == A stronger version of Fubini's theorem for positive functions, where the function is no longer assumed to be measurable but merely that the two iterated integrals are well defined and exist, is independent of ZFC. On the one hand, CH implies that there exists a function on the unit square whose iterated integrals are not equal — the function is simply the indicator function of an ordering of [0, 1] equivalent to a well ordering of the cardinal ω1. A similar example can be constructed using MA. On the other hand, the consistency of the strong Fubini theorem was first shown by Friedman. It can also be deduced from a variant of Freiling's axiom of symmetry. == Topology == The Normal Moore Space conjecture, namely that every normal


id: list-of-euclidean-uniform-tilings-20260505-0
file: data/en.wikipedia.org/wiki/List_of_Euclidean_uniform_tilings-0.md
category: reference
title: List of Euclidean uniform tilings
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_Euclidean_uniform_tilings
date_saved: 2026-05-05T08:17:54.404656+00:00
instance: kb-cron
parent: list-of-euclidean-uniform-tilings-20260505-0
summary:
This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings. There are three regular and eight semiregular tilings in the plane. The semiregular tilings form new tilings from their duals, each made from one type of irregular face. John Conway called these uniform duals Catalan tilings, in parallel to the Catalan solid polyhedra. Uniform tilings are listed by their vertex configuration, the sequence of faces that exist on each vertex. For example 4.8.8 means one square and two octagons on a vertex. These 11 uniform tilings have 32 different uniform colorings. A uniform coloring allows identical sided polygons at a vertex to be colored differently, while still maintaining vertex-uniformity and transformational congruence between vertices. (Note: Some of the tiling images shown below are not color-uniform.) In addition to the 11 convex uniform tilings, there are also 14 known nonconvex tilings, using star polygons, and reverse orientation vertex configurations. A further 28 uniform tilings are known using apeirogons. If zigzags are also allowed, there are 23 more known uniform tilings and 10 more known families depending on a parameter: in 8 cases the parameter is continuous, and in the other 2 it


id: list-of-uniform-polyhedra-20260505-0
file: data/en.wikipedia.org/wiki/List_of_uniform_polyhedra-0.md
category: reference
title: List of uniform polyhedra
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_uniform_polyhedra
date_saved: 2026-05-05T08:17:55.737868+00:00
instance: kb-cron
parent: list-of-uniform-polyhedra-20260505-0
summary:
In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both. This list includes these: all 75 nonprismatic uniform polyhedra; a few representatives of the infinite sets of prisms and antiprisms; one degenerate polyhedron, Skilling's figure with overlapping edges. It was proven in Sopov (1970) that there are only 75 uniform polyhedra other than the infinite families of prisms and antiprisms. John Skilling discovered an overlooked degenerate example, by relaxing the condition that only two faces may meet at an edge. This is a degenerate uniform polyhedron rather than a uniform polyhedron, because some pairs of edges coincide. Not included are: The uniform polyhedron compounds. 40 potential uniform polyhedra with degenerate vertex figures which have overlapping edges (not counted by Coxeter); The uniform tilings (infinite polyhedra) 11 Euclidean convex uniform


id: uniform-tilings-in-hyperbolic-plane-20260505-0
file: data/en.wikipedia.org/wiki/Uniform_tilings_in_hyperbolic_plane-0.md
category: reference
title: Uniform tilings in hyperbolic plane
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Uniform_tilings_in_hyperbolic_plane
date_saved: 2026-05-05T08:17:57.549662+00:00
instance: kb-cron
parent: uniform-tilings-in-hyperbolic-plane-20260505-0
summary:
In hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic plane which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the tiling has a high degree of rotational and translational symmetry. Uniform tilings can be identified by their vertex configuration, a sequence of numbers representing the number of sides of the polygons around each vertex. For example, 7.7.7 represents the heptagonal tiling which has 3 heptagons around each vertex. It is also regular since all the polygons are the same size, so it can also be given the Schläfli symbol {7,3}. Uniform tilings may be regular (if also face- and edge-transitive), quasi-regular (if edge-transitive but not face-transitive) or semi-regular (if neither edge- nor face-transitive). For right triangles (p q 2), there are two regular tilings, represented by Schläfli symbol {p,q} and {q,p}. == Wythoff construction == There are an infinite number of uniform tilings based on the Schwarz triangles (p q r) where ⁠1/p⁠ + ⁠1/q⁠ + ⁠1/r⁠ < 1, where p, q, r are


id: uniform-tilings-in-hyperbolic-plane-20260505-1
file: data/en.wikipedia.org/wiki/Uniform_tilings_in_hyperbolic_plane-1.md
category: reference
title: Uniform tilings in hyperbolic plane
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Uniform_tilings_in_hyperbolic_plane
date_saved: 2026-05-05T08:17:57.549662+00:00
instance: kb-cron
parent: uniform-tilings-in-hyperbolic-plane-20260505-0
summary:
=== (4 3 3) === The (4 3 3) triangle group, Coxeter group [(4,3,3)], orbifold (*433) contains these uniform tilings. Without right angles in the fundamental triangle, the Wythoff constructions are slightly different. For instance in the (4,3,3) triangle family, the snub form has six polygons around a vertex and its dual has hexagons rather than pentagons. In general the vertex figure of a snub tiling in a triangle (p,q,r) is p. 3.q.3.r.3, being 4.3.3.3.3.3 in this case below. === (4 4 3) === The (4 4 3) triangle group, Coxeter group [(4,4,3)], orbifold (*443) contains these uniform tilings. === (4 4 4) === The (4 4 4) triangle group, Coxeter group [(4,4,4)], orbifold (*444) contains these uniform tilings. === (5 3 3) === The (5 3 3) triangle group, Coxeter group [(5,3,3)], orbifold (*533) contains these uniform tilings. === (5 4 3) === The (5 4 3) triangle group, Coxeter group [(5,4,3)], orbifold (*543) contains these uniform tilings. === (5 4 4) === The (5 4 4) triangle group, Coxeter group [(5,4,4)], orbifold (*544) contains these uniform tilings. === (6 3 3) === The (6 3 3) triangle group, Coxeter group [(6,3,3)], orbifold (*633) contains these uniform tilings. ===


id: list-of-united-states-regional-mathematics-competitions-20260505-0
file: data/en.wikipedia.org/wiki/List_of_United_States_regional_mathematics_competitions-0.md
category: reference
title: List of United States regional mathematics competitions
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_United_States_regional_mathematics_competitions
date_saved: 2026-05-05T08:17:58.773121+00:00
instance: kb-cron
parent: list-of-united-states-regional-mathematics-competitions-20260505-0
summary:
Many math competitions in the United States have regional restrictions. Of these, most are statewide. For a more complete list, please visit here . The contests include: == Alabama == Alabama Statewide High School Mathematics Contest Virgil Grissom High School Math Tournament Vestavia Hills High School Math Tournament == Arizona == Great Plains Math League AATM State High School Contest == California == Bay Area Math Olympiad Berkeley Math Tournament Lawrence Livermore National Laboratories Annual High School Math Challenge Cal Poly Math Contest and Trimathlon [1] Polya Competition Bay Area Math Meet College of Creative Studies Math Competition LA Math Cup Math Day at the Beach hosted by CSULB[2] Math Field Day for San Diego Middle Schools Mesa Day Math Contest at UC Berkeley Santa Barbara County Math Superbowl Pomona College Mathematical Talent Search Redwood Empire Mathematics Tournament hosted by Humboldt State (middle and high school) San Diego Math League and San Diego Math Olympiad hosted by the San Diego Math Circle Santa Clara University High School Mathematics Contest Southern California Mathematics Competition, hosted at USC Stanford Mathematics Tournament UCSD/GSDMC High School Honors Mathematics Contest == Colorado == Colorado Mathematics Olympiad == District of Columbia == Moody's Mega Math ==


id: list-of-variational-topics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_variational_topics-0.md
category: reference
title: List of variational topics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_variational_topics
date_saved: 2026-05-05T08:17:59.915350+00:00
instance: kb-cron
parent: list-of-variational-topics-20260505-0
summary:
This is a list of variational topics in from mathematics and physics. See calculus of variations for a general introduction. Action (physics) Averaged Lagrangian Brachistochrone curve Calculus of variations Catenoid Cycloid Dirichlet principle Euler–Lagrange equation cf. Action (physics) Fermat's principle Functional (mathematics) Functional derivative Functional integral Geodesic Isoperimetry Lagrangian Lagrangian mechanics Legendre transformation Luke's variational principle Minimal surface Morse theory Noether's theorem Path integral formulation Plateau's problem Prime geodesic Principle of least action Soap bubble Soap film Tautochrone curve


id: vector-algebra-relations-20260505-0
file: data/en.wikipedia.org/wiki/Vector_algebra_relations-0.md
category: reference
title: Vector algebra relations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vector_algebra_relations
date_saved: 2026-05-05T08:18:01.266487+00:00
instance: kb-cron
parent: vector-algebra-relations-20260505-0
summary:
The following are important identities in vector algebra. Identities that only involve the magnitude of a vector ‖ A ‖ {\displaystyle \|\mathbf {A} \|} and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there. Most of these relations can be dated to founder of vector calculus Josiah Willard Gibbs, if not earlier. == Magnitudes == The magnitude of a vector A can be expressed using the dot product: ‖ A ‖ 2 = A ⋅ A {\displaystyle \|\mathbf {A} \|^{2}=\mathbf {A\cdot A} } In three-dimensional Euclidean space, the magnitude of a vector is determined from its three components using Pythagoras' theorem: ‖ A ‖ 2 = A 1 2 + A 2 2 + A 3 2 {\displaystyle \|\mathbf {A} \|^{2}=A_{1}^{2}+A_{2}^{2}+A_{3}^{2}} == Inequalities == The Cauchy–Schwarz inequality: A ⋅ B ≤ ‖ A ‖ ‖ B ‖ {\displaystyle \mathbf {A} \cdot \mathbf {B} \leq \left\|\mathbf {A} \right\|\left\|\mathbf {B} \right\|} The triangle inequality: ‖ A + B ‖ ≤ ‖ A ‖ + ‖ B ‖ {\displaystyle \|\mathbf {A+B} \|\leq \|\mathbf {A}


id: vector-algebra-relations-20260505-1
file: data/en.wikipedia.org/wiki/Vector_algebra_relations-1.md
category: reference
title: Vector algebra relations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vector_algebra_relations
date_saved: 2026-05-05T08:18:01.266487+00:00
instance: kb-cron
parent: vector-algebra-relations-20260505-0
summary:
== Addition and multiplication of vectors == Commutativity of addition: A + B = B + A {\displaystyle \mathbf {A} +\mathbf {B} =\mathbf {B} +\mathbf {A} } . Commutativity of scalar product: A ⋅ B = B ⋅ A {\displaystyle \mathbf {A} \cdot \mathbf {B} =\mathbf {B} \cdot \mathbf {A} } . Anticommutativity of cross product: A × B = − ( B × A ) {\displaystyle \mathbf {A} \times \mathbf {B} =\mathbf {-} (\mathbf {B} \times \mathbf {A} )} . Distributivity of multiplication by a scalar over addition: c ( A + B ) = c A + c B {\displaystyle c(\mathbf {A} +\mathbf {B} )=c\mathbf {A} +c\mathbf {B} } . Distributivity of scalar product over addition: ( A + B ) ⋅ C = A ⋅ C + B ⋅ C {\displaystyle \left(\mathbf {A} +\mathbf {B} \right)\cdot \mathbf {C} =\mathbf {A} \cdot \mathbf {C} +\mathbf {B} \cdot \mathbf {C} } . Distributivity of vector product over addition: ( A + B ) × C = A × C + B × C {\displaystyle (\mathbf {A} +\mathbf {B} )\times \mathbf {C} =\mathbf {A} \times \mathbf {C} +\mathbf {B} \times \mathbf {C} } . Scalar triple product: A ⋅ (


id: vector-algebra-relations-20260505-2
file: data/en.wikipedia.org/wiki/Vector_algebra_relations-2.md
category: reference
title: Vector algebra relations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vector_algebra_relations
date_saved: 2026-05-05T08:18:01.266487+00:00
instance: kb-cron
parent: vector-algebra-relations-20260505-0
summary:
A consequence of the previous equation: | A B C | D = ( A ⋅ D ) ( B × C ) + ( B ⋅ D ) ( C × A ) + ( C ⋅ D ) ( A × B ) . {\displaystyle |\mathbf {A} \,\mathbf {B} \,\mathbf {C} |\,\mathbf {D} =(\mathbf {A} \cdot \mathbf {D} )\left(\mathbf {B} \times \mathbf {C} \right)+\left(\mathbf {B} \cdot \mathbf {D} \right)\left(\mathbf {C} \times \mathbf {A} \right)+\left(\mathbf {C} \cdot \mathbf {D} \right)\left(\mathbf {A} \times \mathbf {B} \right).} In 3 dimensions, a vector D can be expressed in terms of basis vectors {A,B,C} as: D = D ⋅ ( B × C ) | A B C | A + D ⋅ ( C × A ) | A B C | B + D ⋅ ( A × B ) | A B C | C . {\displaystyle \mathbf {D} \ =\ {\frac {\mathbf {D} \cdot (\mathbf {B} \times \mathbf {C} )}{|\mathbf {A} \,\mathbf {B} \,\mathbf {C} |}}\ \mathbf {A} +{\frac {\mathbf {D} \cdot (\mathbf {C} \times \mathbf {A} )}{|\mathbf {A} \,\mathbf {B} \,\mathbf {C} |}}\ \mathbf {B} +{\frac {\mathbf {D} \cdot (\mathbf {A} \times \mathbf {B} )}{|\mathbf {A} \,\mathbf {B}


id: vector-calculus-identities-20260505-0
file: data/en.wikipedia.org/wiki/Vector_calculus_identities-0.md
category: reference
title: Vector calculus identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vector_calculus_identities
date_saved: 2026-05-05T08:18:02.786492+00:00
instance: kb-cron
parent: vector-calculus-identities-20260505-0
summary:
The following are important identities involving derivatives and integrals in vector calculus. == Operator notation == === Gradient === For a function f ( x , y , z ) {\displaystyle f(x,y,z)} in three-dimensional Cartesian coordinate variables, the gradient is the vector field: grad ⁡ ( f ) = ∇ f = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) f = ∂ f ∂ x i + ∂ f ∂ y j + ∂ f ∂ z k {\displaystyle \operatorname {grad} (f)=\nabla f={\begin{pmatrix}\displaystyle {\frac {\partial }{\partial x}},\ {\frac {\partial }{\partial y}},\ {\frac {\partial }{\partial z}}\end{pmatrix}}f={\frac {\partial f}{\partial x}}\mathbf {i} +{\frac {\partial f}{\partial y}}\mathbf {j} +{\frac {\partial f}{\partial z}}\mathbf {k} } where i, j, k are the standard unit vectors for the x, y, z-axes. More generally, for a function of n variables ψ ( x 1 , … , x n ) {\displaystyle \psi (x_{1},\ldots ,x_{n})} , also called a scalar field, the gradient is the vector field: ∇ ψ = ( ∂ ∂ x 1 , … , ∂ ∂ x n ) ψ = ∂ ψ ∂ x 1 e 1 + ⋯ + ∂ ψ ∂ x n e n {\displaystyle


id: vector-calculus-identities-20260505-1
file: data/en.wikipedia.org/wiki/Vector_calculus_identities-1.md
category: reference
title: Vector calculus identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vector_calculus_identities
date_saved: 2026-05-05T08:18:02.786492+00:00
instance: kb-cron
parent: vector-calculus-identities-20260505-0
summary:
curl ⁡ F = ∇ × F = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) × ( F x , F y , F z ) = | i j k ∂ ∂ x ∂ ∂ y ∂ ∂ z F x F y F z | = ( ∂ F z ∂ y − ∂ F y ∂ z ) i + ( ∂ F x ∂ z − ∂ F z ∂ x ) j + ( ∂ F y ∂ x − ∂ F x ∂ y ) k {\displaystyle {\begin{aligned}\operatorname {curl} \mathbf {F} &=\nabla \times \mathbf {F} ={\begin{pmatrix}\displaystyle {\frac {\partial }{\partial x}},\ {\frac {\partial }{\partial y}},\ {\frac {\partial }{\partial z}}\end{pmatrix}}\times {\begin{pmatrix}F_{x},\ F_{y},\ F_{z}\end{pmatrix}}\\[1em]&={\begin{vmatrix}\mathbf {i} &\mathbf {j} &\mathbf {k} \\{\frac {\partial }{\partial x}}&{\frac {\partial }{\partial y}}&{\frac {\partial }{\partial z}}\\F_{x}&F_{y}&F_{z}\end{vmatrix}}\\[1em]&=\left({\frac {\partial F_{z}}{\partial y}}-{\frac {\partial F_{y}}{\partial z}}\right)\mathbf {i} +\left({\frac {\partial F_{x}}{\partial z}}-{\frac {\partial F_{z}}{\partial x}}\right)\mathbf {j} +\left({\frac {\partial F_{y}}{\partial x}}-{\frac {\partial F_{x}}{\partial y}}\right)\mathbf {k} \end{aligned}}} where i, j, and k are the unit vectors for the x-, y-, and z-axes, respectively. As the name implies the curl is a measure of how much nearby vectors tend in a circular direction. In Einstein notation,


id: vector-calculus-identities-20260505-2
file: data/en.wikipedia.org/wiki/Vector_calculus_identities-2.md
category: reference
title: Vector calculus identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vector_calculus_identities
date_saved: 2026-05-05T08:18:02.786492+00:00
instance: kb-cron
parent: vector-calculus-identities-20260505-0
summary:
∇ ⋅ ( A × B ) = ∇ A ⋅ ( A × B ) + ∇ B ⋅ ( A × B ) = ( ∇ A × A ) ⋅ B + ( ∇ B × A ) ⋅ B = ( ∇ A × A ) ⋅ B − ( A × ∇ B ) ⋅ B = ( ∇ A × A ) ⋅ B − A ⋅ ( ∇ B × B ) = ( ∇ × A ) ⋅ B − A ⋅ ( ∇ × B ) {\displaystyle {\begin{aligned}\nabla \cdot (\mathbf {A} \times \mathbf {B} )&=\nabla _{\mathbf {A} }\cdot (\mathbf {A} \times \mathbf {B} )+\nabla _{\mathbf {B} }\cdot (\mathbf {A} \times \mathbf {B} )\\[2pt]&=(\nabla _{\mathbf {A} }\times \mathbf {A} )\cdot \mathbf {B} +(\nabla _{\mathbf {B} }\times \mathbf {A} )\cdot \mathbf {B} \\[2pt]&=(\nabla _{\mathbf {A} }\times \mathbf {A} )\cdot \mathbf {B} -(\mathbf {A} \times \nabla _{\mathbf {B} })\cdot \mathbf {B} \\[2pt]&=(\nabla _{\mathbf {A} }\times \mathbf {A} )\cdot \mathbf {B} -\mathbf {A} \cdot (\nabla _{\mathbf {B} }\times \mathbf {B} )\\[2pt]&=(\nabla \times \mathbf {A} )\cdot \mathbf {B} -\mathbf {A} \cdot (\nabla \times \mathbf {B} )\end{aligned}}} An alternative method is to use the Cartesian components of


id: vector-calculus-identities-20260505-3
file: data/en.wikipedia.org/wiki/Vector_calculus_identities-3.md
category: reference
title: Vector calculus identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vector_calculus_identities
date_saved: 2026-05-05T08:18:02.786492+00:00
instance: kb-cron
parent: vector-calculus-identities-20260505-0
summary:
For the remainder of this article, Feynman subscript notation will be used where appropriate. == First derivative identities == For scalar fields ψ {\displaystyle \psi } , ϕ {\displaystyle \phi } and vector fields A {\displaystyle \mathbf {A} } , B {\displaystyle \mathbf {B} } , we have the following derivative identities. === Distributive properties === === First derivative associative properties === === Product rule for multiplication by a scalar === We have the following generalizations of the product rule in single-variable calculus. === Quotient rule for division by a scalar === === Chain rule === Let f ( x ) {\displaystyle f(x)} be a one-variable function from scalars to scalars, r ( t ) = ( x 1 ( t ) , … , x n ( t ) ) {\displaystyle \mathbf {r} (t)=(x_{1}(t),\ldots ,x_{n}(t))} a parametrized curve, ϕ : R n → R {\displaystyle \phi \!:\mathbb {R} ^{n}\to \mathbb {R} } a function from vectors to scalars, and A : R n → R n {\displaystyle \mathbf {A} \!:\mathbb {R} ^{n}\to \mathbb {R} ^{n}} a vector field. We have the following special cases of the multi-variable chain rule. For a vector transformation u : R n → R


id: vector-calculus-identities-20260505-4
file: data/en.wikipedia.org/wiki/Vector_calculus_identities-4.md
category: reference
title: Vector calculus identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vector_calculus_identities
date_saved: 2026-05-05T08:18:02.786492+00:00
instance: kb-cron
parent: vector-calculus-identities-20260505-0
summary:
=== Curl of divergence is not defined === The divergence of a vector field A is a scalar, and the curl of a scalar quantity is undefined. Therefore, ∇ × ( ∇ ⋅ A ) is undefined. {\displaystyle \nabla \times (\nabla \cdot \mathbf {A} ){\text{ is undefined.}}} === Second derivative associative properties === === A mnemonic === The figure to the right is a mnemonic for some of these identities. The abbreviations used are: D: divergence, C: curl, G: gradient, L: Laplacian, CC: curl of curl. Each arrow is labeled with the result of an identity, specifically, the result of applying the operator at the arrow's tail to the operator at its head. The blue circle in the middle means curl of curl exists, whereas the other two red circles (dashed) mean that DD and GG do not exist. == Summary of important identities == === Differentiation === ==== Gradient ==== ==== Divergence ==== ==== Curl ==== ==== Vector-dot-Del Operator ==== ==== Second derivatives ==== ==== Third derivatives ==== === Integration === Below, the curly symbol ∂ means "boundary of" a surface or solid. ==== Surface–volume integrals ==== In the following surface–volume integral theorems, V denotes a three-dimensional volume with


id: vector-calculus-identities-20260505-5
file: data/en.wikipedia.org/wiki/Vector_calculus_identities-5.md
category: reference
title: Vector calculus identities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vector_calculus_identities
date_saved: 2026-05-05T08:18:02.786492+00:00
instance: kb-cron
parent: vector-calculus-identities-20260505-0
summary:
∮ ∂ S A × ( B × d ℓ ) = ∬ S ( ∇ × ( A B T ) ) ⋅ d S + ∬ S ( ∇ ⋅ ( B A T ) ) × d S {\displaystyle \oint _{\partial S}\mathbf {A} \times (\mathbf {B} \times d{\boldsymbol {\ell }})\ =\ \iint _{S}\left(\nabla \times \left(\mathbf {A} \mathbf {B} ^{\textsf {T}}\right)\right)\cdot d\mathbf {S} +\iint _{S}\left(\nabla \cdot \left(\mathbf {B} \mathbf {A} ^{\textsf {T}}\right)\right)\times d\mathbf {S} } ∮ ∂ S ( B ⋅ d ℓ ) A = ∬ S ( d S ⋅ [ ∇ × B − B × ∇ ] ) A {\displaystyle \oint _{\partial S}(\mathbf {B} \cdot d{\boldsymbol {\ell }})\mathbf {A} =\iint _{S}(d\mathbf {S} \cdot \left[\nabla \times \mathbf {B} -\mathbf {B} \times \nabla \right])\mathbf {A} } Integration around a closed curve in the clockwise sense is the negative of the same line integral in the counterclockwise sense (analogous to interchanging the limits in a definite integral): ==== Endpoint-curve integrals ==== In the following endpoint–curve integral theorems, P denotes a 1d open path with signed 0d boundary points q − p = ∂ P {\displaystyle \mathbf {q} -\mathbf {p} =\partial P} and integration along P is from


id: list-of-vector-spaces-in-mathematics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_vector_spaces_in_mathematics-0.md
category: reference
title: List of vector spaces in mathematics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_vector_spaces_in_mathematics
date_saved: 2026-05-05T08:18:04.096795+00:00
instance: kb-cron
parent: list-of-vector-spaces-in-mathematics-20260505-0
summary:
This is a list of vector spaces in abstract mathematics, by Wikipedia page. Banach space Besov space Bochner space Dual space Euclidean space Fock space Fréchet space Hardy space Hilbert space Hölder space LF-space Lp space Minkowski space Montel space Morrey–Campanato space Orlicz space Riesz space Schwartz space Sobolev space Tsirelson space


id: list-of-wavelet-related-transforms-20260505-0
file: data/en.wikipedia.org/wiki/List_of_wavelet-related_transforms-0.md
category: reference
title: List of wavelet-related transforms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_wavelet-related_transforms
date_saved: 2026-05-05T08:18:06.741131+00:00
instance: kb-cron
parent: list-of-wavelet-related-transforms-20260505-0
summary:
A list of wavelet related transforms: Continuous wavelet transform (CWT) Discrete wavelet transform (DWT) Multiresolution analysis (MRA) Lifting scheme Binomial QMF (BQMF) Fast wavelet transform (FWT) Complex wavelet transform Non or undecimated wavelet transform, the downsampling is omitted Newland transform, an orthonormal basis of wavelets is formed from appropriately constructed top-hat filters in frequency space Wavelet packet decomposition (WPD), detail coefficients are decomposed and a variable tree can be formed Stationary wavelet transform (SWT), no downsampling and the filters at each level are different e-decimated discrete wavelet transform, depends on if the even or odd coefficients are selected in the downsampling Second generation wavelet transform (SGWT), filters and wavelets are not created in the frequency domain Dual-tree complex wavelet transform (DTCWT), two trees are used for decomposion to produce the real and complex coefficients WITS: Where Is The Starlet, a collection of a hundredth of wavelet names in -let and associated multiscale, directional, geometric, representations, from activelets to x-lets through bandelets, chirplets, contourlets, curvelets, noiselets, wedgelets ...


id: list-of-wenninger-polyhedron-models-20260505-0
file: data/en.wikipedia.org/wiki/List_of_Wenninger_polyhedron_models-0.md
category: reference
title: List of Wenninger polyhedron models
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_Wenninger_polyhedron_models
date_saved: 2026-05-05T08:18:08.055382+00:00
instance: kb-cron
parent: list-of-wenninger-polyhedron-models-20260505-0
summary:
This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes. It contains the 75 nonprismatic uniform polyhedra, as well as 44 stellated forms of the convex regular and quasiregular polyhedra. Models listed here can be cited as "Wenninger Model Number N", or WN for brevity. The polyhedra are grouped in 5 tables: Regular (1–5), Semiregular (6–18), regular star polyhedra (20–22,41), Stellations and compounds (19–66), and uniform star polyhedra (67–119). The four regular star polyhedra are listed twice because they belong to both the uniform polyhedra and stellation groupings. == Platonic solids (regular convex polyhedra) W1 to W5 == == Archimedean solids (Semiregular) W6 to W18 == == Kepler–Poinsot polyhedra (Regular star polyhedra) W20, W21, W22 and W41 == == Stellations: models W19 to W66 == === Stellations of octahedron === === Stellations of dodecahedron === === Stellations of icosahedron === === Stellations of cuboctahedron === === Stellations of icosidodecahedron === == Uniform nonconvex solids


id: list-of-zeta-functions-20260505-0
file: data/en.wikipedia.org/wiki/List_of_zeta_functions-0.md
category: reference
title: List of zeta functions
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_zeta_functions
date_saved: 2026-05-05T08:18:09.230852+00:00
instance: kb-cron
parent: list-of-zeta-functions-20260505-0
summary:
In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function ζ ( s ) = ∑ n = 1 ∞ 1 n s . {\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}.} Zeta functions include: Airy zeta function, related to the zeros of the Airy function Arakawa–Kaneko zeta function Arithmetic zeta function Artin–Mazur zeta function of a dynamical system Barnes zeta function or double zeta function Beurling zeta function of Beurling generalized primes Dedekind zeta function of a number field Duursma zeta function of error-correcting codes Epstein zeta function of a quadratic form Goss zeta function of a function field Hasse–Weil zeta function of a variety Height zeta function of a variety Hurwitz zeta function, a generalization of the Riemann zeta function Igusa zeta function Ihara zeta function of a graph L-function, a "twisted" zeta function Lefschetz zeta function of a morphism Lerch zeta function, a generalization of the Riemann zeta function Local zeta function of a characteristic-p variety Matsumoto zeta function Minakshisundaram–Pleijel zeta function of a Laplacian Motivic zeta function of a motive Multiple zeta function, or Mordell–Tornheim zeta function of several variables p-adic zeta function of a p-adic number Prime zeta function,


id: index-of-meteorology-articles-20260505-0
file: data/en.wikipedia.org/wiki/Index_of_meteorology_articles-0.md
category: reference
title: Index of meteorology articles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Index_of_meteorology_articles
date_saved: 2026-05-05T08:18:10.971529+00:00
instance: kb-cron
parent: index-of-meteorology-articles-20260505-0
summary:
This is a list of meteorology topics. The terms relate to meteorology, the interdisciplinary scientific study of the atmosphere that focuses on weather processes and forecasting. (see also: List of meteorological phenomena) == A == advection aeroacoustics aerobiology aerology air parcel (in meteorology) air quality index (AQI) airshed (in meteorology) American Geophysical Union (AGU) American Meteorological Society (AMS) anabatic wind anemometer annular hurricane anticyclone (in meteorology) apparent wind Atlantic Oceanographic and Meteorological Laboratory (AOML) Atlantic hurricane season atmometer atmosphere Atmospheric Model Intercomparison Project (AMIP) Atmospheric Radiation Measurement (ARM) (atmospheric boundary layer [ABL]) planetary boundary layer (PBL) atmospheric chemistry atmospheric circulation atmospheric convection atmospheric dispersion modeling atmospheric electricity atmospheric icing atmospheric physics atmospheric pressure atmospheric sciences atmospheric stratification atmospheric thermodynamics atmospheric window (see under Threats) == B == ball lightning balloon (aircraft) baroclinity barotropicity barometer ("to measure atmospheric pressure") berg wind biometeorology blizzard bomb (meteorology) buoyancy Bureau of Meteorology (in Australia) == C == Canada Weather Extremes Canadian Hurricane Centre (CHC) Cape Verde-type hurricane capping inversion (in meteorology) (see "severe thunderstorms" in paragraph 5) carbon cycle carbon fixation carbon flux carbon monoxide (see under Atmospheric presence) ceiling balloon ("to determine the height of the base of clouds above ground level") ceilometer


id: index-of-meteorology-articles-20260505-1
file: data/en.wikipedia.org/wiki/Index_of_meteorology_articles-1.md
category: reference
title: Index of meteorology articles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Index_of_meteorology_articles
date_saved: 2026-05-05T08:18:10.971529+00:00
instance: kb-cron
parent: index-of-meteorology-articles-20260505-0
summary:
== E == Earth's atmosphere Earth's magnetic field Earth System Research Laboratories (ESRL) economics of global warming Emagram effect of Hurricane Katrina on New Orleans (see also Hurricane Katrina effects by region) effect of sun angle on climate Energy meteorology Enhanced Fujita scale (EF scale) eolian processes equator (see under Equatorial seasons and climate) equilibrium level (EL) equivalent potential temperature equivalent temperature European Centre for Medium-Range Weather Forecasts (ECMWF) European Climate Change Programme (ECCP) European emission standards (for motor vehicles) European Severe Storms Laboratory (ESSL) European windstorm evaporation evaporative cooler evaporative cooling evaporite (a mineral sediment resulting from evaporation of saline water) evapotranspiration (ET) (sum of evaporation and plant transpiration) exhaust gas recirculation (EGR) (exhaust gas recycling) exosphere (layer of atmosphere) extratropical cyclone (mid-latitude cyclone) extreme weather extremes on Earth == F == fire whirl firestorm fog forensic meteorology free convective layer (FCL) freezing rain (front [meteorology]: see) surface weather analysis frontogenesis frontolysis frost frost creep (frost heave) frost flowers (frost castles) (ice castles) (ice ribbons) (ice blossoms) frost heaving (frost heave) frost law frost line (frost point: see) dew point (dewpoint) frostbite Fujita scale (F scale) (for measuring tornadoes) fulgurite (full lunar eclipse: see) lunar eclipse full-spectrum light funnel


id: index-of-meteorology-articles-20260505-2
file: data/en.wikipedia.org/wiki/Index_of_meteorology_articles-2.md
category: reference
title: Index of meteorology articles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Index_of_meteorology_articles
date_saved: 2026-05-05T08:18:10.971529+00:00
instance: kb-cron
parent: index-of-meteorology-articles-20260505-0
summary:
== N == NASA Clean Air Study NASA Earth Observatory NASA World Wind (virtual globe) National Ambient Air Quality Standards (NAAQS) (in the US) National Center for Atmospheric Research (NCAR) (in the US) National Centers for Environmental Prediction (NCEP) (in the US) National Climatic Data Center (NCDC) (in the US) National Emissions Standards for Hazardous Air Pollutants (NESHAPS) (in the US) (National Environmental Satellite, Data and Information Service: see) National Oceanic and Atmospheric Administration (NOAA) (in the US) National Geomagnetism Program (in the US) National Hurricane Center (NHC) (in the US) National Map (in the US) National Oceanic and Atmospheric Administration (NOAA) (in the US) (National Severe Storms Forecast Center [NSSFC]: renamed) Storm Prediction Center (SPC) (in the US) National Severe Storms Laboratory (NSSL) (in the US) National Snow and Ice Data Center (NSIDC) (in the US) National Solar Observatory (in the US) National Weather Association (NWA) (in the US) National Weather Center (NWC) (in the US) National Weather Service bulletin for New Orleans region (at 10:11 a.m., August 28, 2005) National Weather Service (NWS) nautical almanac nephology nephoscope night sky nimbus cloud nitrogen cycle (nitrogen pollution: see) eutrophication (see under Atmospheric deposition) NOAA Weather Radio All Hazards (NWR) (of


id: outline-of-meteorology-20260505-0
file: data/en.wikipedia.org/wiki/Outline_of_meteorology-0.md
category: reference
title: Outline of meteorology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Outline_of_meteorology
date_saved: 2026-05-05T08:18:12.231405+00:00
instance: kb-cron
parent: outline-of-meteorology-20260505-0
summary:
The following outline is provided as an overview of and topical guide to the field of Meteorology. Meteorology The interdisciplinary, scientific study of the Earth's atmosphere with the primary focus being to understand, explain, and forecast weather events. Meteorology, is applied to and employed by a wide variety of diverse fields, including the military, energy production, transport, agriculture, and construction. == Essence of meteorology == Meteorology Climate – the average and variations of weather in a region over long periods of time. Meteorology – the interdisciplinary scientific study of the atmosphere that focuses on weather processes and forecasting (in contrast with climatology). Weather – the set of all the phenomena in a given atmosphere at a given time. == Branches of meteorology == Microscale meteorology – the study of atmospheric phenomena about 1 km or less, smaller than mesoscale, including small and generally fleeting cloud "puffs" and other small cloud features Mesoscale meteorology – the study of weather systems about 5 kilometers to several hundred kilometers, smaller than synoptic scale systems but larger than microscale and storm-scale cumulus systems, such as sea breezes, squall lines, and mesoscale convective complexes Synoptic scale meteorology – is a horizontal length scale of the


id: outline-of-meteorology-20260505-1
file: data/en.wikipedia.org/wiki/Outline_of_meteorology-1.md
category: reference
title: Outline of meteorology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Outline_of_meteorology
date_saved: 2026-05-05T08:18:12.231405+00:00
instance: kb-cron
parent: outline-of-meteorology-20260505-0
summary:
History of weather forecasting – prior to the invention of meteorological instruments, weather analysis and prediction relied on pattern recognition, which was not always reliable History of surface weather analysis – initially used to study storm behavior, now used to explain current weather and as an aid in short term weather forecasting == Meteorological phenomena == Atmospheric pressure – the pressure at any given point in the Earth's atmosphere Cloud – a visible mass of droplets or frozen crystals floating in the atmosphere above the surface of a planet Rain – precipitation in which separate drops of water fall to the Earth from clouds, a product of the condensation of atmospheric water vapor Snow – precipitation in the form of crystalline water ice, consisting of a multitude of snowflakes that fall from clouds Freezing rain – precipitation that falls from a cloud as snow, melts completely on its way down, then passes through a layer of below-freezing air becoming supercooled, at which point it will freeze upon impact with any object encountered Sleet – term used in the United States and Canada for precipitation consisting of small, translucent ice balls, usually smaller than hailstones Tropical cyclone – a storm system


id: list-of-atlantic-hurricane-records-20260505-0
file: data/en.wikipedia.org/wiki/List_of_Atlantic_hurricane_records-0.md
category: reference
title: List of Atlantic hurricane records
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_Atlantic_hurricane_records
date_saved: 2026-05-05T08:18:13.570754+00:00
instance: kb-cron
parent: list-of-atlantic-hurricane-records-20260505-0
summary:
As of November 2025, there have been 1,753 tropical cyclones of at least tropical storm intensity, 972 at hurricane intensity, and 342 at major hurricane intensity within the Atlantic Ocean since 1851, the first Atlantic hurricane season to be included in the official Atlantic tropical cyclone record. Though a majority of these cyclones have fallen within climatological averages, prevailing atmospheric conditions occasionally lead to anomalous tropical systems which at times reach extremes in statistical record-keeping including in duration and intensity. The scope of this list is limited to tropical cyclone records solely within the North Atlantic Ocean and is subdivided by their reason for notability. == Tropical cyclogenesis == === Most active / least active Atlantic hurricane seasons === Most Atlantic hurricane seasons prior to the weather satellite era include seven or fewer recorded tropical storms or hurricanes. As the usage of satellite data was not available until the mid-1960s, early storm counts are less reliable. Before the advent of the airplane or means of tracking storms, the ones recorded were storms that affected mainly populated areas. An undercount bias of zero to six tropical cyclones per year between 1851 and 1885 and zero to four per year between 1886


id: list-of-atlantic-hurricane-records-20260505-1
file: data/en.wikipedia.org/wiki/List_of_Atlantic_hurricane_records-1.md
category: reference
title: List of Atlantic hurricane records
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_Atlantic_hurricane_records
date_saved: 2026-05-05T08:18:13.570754+00:00
instance: kb-cron
parent: list-of-atlantic-hurricane-records-20260505-0
summary:
Generally speaking, the intensity of a tropical cyclone is determined by either the storm's maximum sustained winds or lowest barometric pressure. The following table lists the most intense Atlantic hurricanes in terms of their lowest barometric pressure. In terms of wind speed, Allen from 1980 and Melissa from 2025 are tied for the strongest Atlantic tropical cyclones on record, with maximum sustained winds of 190 mph (305 km/h). For many years, it was thought that Hurricane Camille also attained this intensity, but this conclusion was changed in 2014. The original measurements of Camille are suspect since wind speed instrumentation used at the time would likely be damaged by winds of such intensity. Nonetheless, their central pressures are low enough to rank them among the strongest recorded Atlantic hurricanes. This is also why despite there being 2 hurricanes in the month of January, neither of them are ranked here as both of them had a higher pressure than Unnamed Subtropical Storm (2023). Owing to their intensity, the strongest Atlantic hurricanes have all attained Category 5 classification. Hurricane Opal, the most intense Category 4 hurricane recorded, intensified to reach a minimum pressure of 916 mbar (hPa; 27.05 inHg), a pressure typical of


id: list-of-atlantic-hurricane-records-20260505-2
file: data/en.wikipedia.org/wiki/List_of_Atlantic_hurricane_records-2.md
category: reference
title: List of Atlantic hurricane records
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_Atlantic_hurricane_records
date_saved: 2026-05-05T08:18:13.570754+00:00
instance: kb-cron
parent: list-of-atlantic-hurricane-records-20260505-0
summary:
=== Fastest intensification === Fastest intensification from a tropical depression to a hurricane (1-minute sustained surface winds) – 12 hoursHarvey 1981 – 35 mph (55 km/h) to 80 mph (130 km/h) – from 1200 UTC September 12 to 0000 UTC September 13 Fastest intensification from a tropical depression to a Category 5 hurricane (1-minute sustained surface winds) – 54 hoursMilton 2024 – 35 mph (55 km/h) to 175 mph (280 km/h) – from 1200 UTC October 5 to 1800 UTC October 7 Fastest intensification from a tropical storm to a Category 5 hurricane (1-minute sustained surface winds) – 24 hoursWilma 2005 – 70 mph (110 km/h) to 175 mph (275 km/h) – from 0600 UTC October 18 to 0600 UTC October 19 Maximum pressure drop in 12 hours – 83 mbarWilma 2005 – 975 millibars (28.8 inHg) to 892 millibars (26.3 inHg) – from 1800 UTC October 18 to 0600 UTC October 19 Maximum pressure drop in 24 hours – 97 mbarWilma 2005 – 979 millibars (28.9 inHg) to 882 millibars (26.0 inHg) – from 1200 UTC October 18 to 1200 UTC October 19 == Landfall == === Earliest and latest Atlantic landfalls === === Southern and northernmost Atlantic landfalls


id: list-of-countries-by-average-yearly-temperature-20260505-0
file: data/en.wikipedia.org/wiki/List_of_countries_by_average_yearly_temperature-0.md
category: reference
title: List of countries by average yearly temperature
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_countries_by_average_yearly_temperature
date_saved: 2026-05-05T08:18:14.880921+00:00
instance: kb-cron
parent: list-of-countries-by-average-yearly-temperature-20260505-0
summary:
This is a list of countries and sovereign states by temperature. Average yearly temperature is calculated by averaging the minimum and maximum daily temperatures in the country, averaged for the years 1991 – 2020, from World Bank Group, derived from raw gridded climatologies from the Climatic Research Unit. == See also == List of countries by average annual precipitation == References ==


id: list-of-rogue-waves-incidents-20260505-0
file: data/en.wikipedia.org/wiki/List_of_rogue_waves_incidents-0.md
category: reference
title: List of rogue waves incidents
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_rogue_waves_incidents
date_saved: 2026-05-05T08:18:17.503231+00:00
instance: kb-cron
parent: list-of-rogue-waves-incidents-20260505-0
summary:
This list of rogue waves compiles incidents of known and likely rogue waves – also known as freak waves, monster waves, killer waves, and extreme waves. These are dangerous and rare ocean surface waves that unexpectedly reach at least twice the height of the tallest waves around them, and are often described by witnesses as "walls of water". They occur in deep water, usually far out at sea, and are a threat even to capital ships, ocean liners and land structures such as lighthouses. == Background == Anecdotal evidence from mariners' testimonies and incidents of wave damage to ships has long suggested the existence of rogue waves; however, their scientific measurement was positively confirmed only following measurements of the Draupner wave, a rogue wave at the Draupner platform, in the North Sea on 1 January 1995. In this event, minor damage was inflicted on the platform, confirming that the reading was valid. In modern oceanography, rogue waves are defined not as the biggest possible waves at sea, but instead as extreme sized waves for a given sea state. Many of these encounters are only reported in the media, and are not examples of open ocean rogue waves. Often a huge


id: list-of-rogue-waves-incidents-20260505-1
file: data/en.wikipedia.org/wiki/List_of_rogue_waves_incidents-1.md
category: reference
title: List of rogue waves incidents
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_rogue_waves_incidents
date_saved: 2026-05-05T08:18:17.503231+00:00
instance: kb-cron
parent: list-of-rogue-waves-incidents-20260505-0
summary:
On 4 August 1498, during the third voyage of Christopher Columbus, Columbus's ships were in the Gulf of Paria off the southern tip of Trinidad when Columbus heard a tremendous roar from behind his flagship. He observed a wave approaching from astern that was as tall as his ships' masts. Columbus described the wave as lifting his ships higher than anything he ever had experienced before, after which the ships dropped into a huge trough. On 28 September 1853 a huge wave struck the emigrant ship Annie Jane while she was off Barra in the Outer Hebrides. The wave caused the poop deck to collapse, instantly crushing 200 people to death. Annie Jane soon sank, and her 102 survivors were washed ashore on a piece of her deck. On 11 March 1861 at midday the lighthouse on Eagle Island off the west coast of Ireland was struck by a large wave that smashed 23 panes, washing some of the lamps down the stairs, and broken glass damaged the reflectors beyond repair. In order to damage the uppermost portion of the lighthouse, water had to surmount a seaside cliff measuring 40 m (130 ft) in height and a further 26 m


id: list-of-rogue-waves-incidents-20260505-2
file: data/en.wikipedia.org/wiki/List_of_rogue_waves_incidents-2.md
category: reference
title: List of rogue waves incidents
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_rogue_waves_incidents
date_saved: 2026-05-05T08:18:17.503231+00:00
instance: kb-cron
parent: list-of-rogue-waves-incidents-20260505-0
summary:
Water rose as high as the bottom of her lower foretop, filling it with water, sweeping her forward deck clear, smashing her forebridge – much of which was found in pieces on her upper deck – wrecking her chart house, shifting the roof of her conning tower, and flooding her forward main gun turret, mess decks, and flats. Five of her crew died, and 17 others suffered serious injuries. At midnight on 5–6 May 1916 the British polar explorer Ernest Shackleton was at the tiller of the small sailboat James Caird in the Southern Ocean during a storm when he thought he saw the bad weather clearing in the west, astern. He then realized that what he thought was a line of white clouds above a clear dark sky was actually the crest of a single enormous wave that struck and nearly swamped the boat. Shackleton reported that the wave was larger than any he had ever seen before in his 26 years of seafaring. On 29 August 1916 at about 4:40 p.m., the United States Navy armored cruiser USS Memphis was wrecked in Santo Domingo harbor in the Dominican Republic when struck in rapid succession by three waves of


id: list-of-rogue-waves-incidents-20260505-3
file: data/en.wikipedia.org/wiki/List_of_rogue_waves_incidents-3.md
category: reference
title: List of rogue waves incidents
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_rogue_waves_incidents
date_saved: 2026-05-05T08:18:17.503231+00:00
instance: kb-cron
parent: list-of-rogue-waves-incidents-20260505-0
summary:
=== Second half of the 20th century === On 5 February 1963, the French Navy light cruiser Jeanne d'Arc encountered a rogue wave while serving as the training ship of the French Naval Academy. On 12 April 1966, the Italian liner Michelangelo was in the Atlantic Ocean steaming toward New York City in a storm, frequently encountering 20-metre (66 ft) waves, when a giant wave struck her, breaking 18 metres (59 ft) over her bow. It traveled 70 metres (230 ft) aft along her deck and struck her superstructure, smashing 2-centimetre (0.8 in) thick windows on her bridge over 25 metres (82 ft) above the waterline. It tore a hole in the superstructure, killed two passengers instantly, fatally injured a crewman who died a few hours later, and injured over 50 other people, 10 of them gravely. In 1968 the sailing yacht Suhaili was in the Southern Ocean in high winds and a 40-to-50-foot (12 to 15 m) swell when her captain came on deck and sighted a breaking wave approaching from astern which stretched from horizon to horizon and was twice the height of the swell, indicating a height of at least 80 feet (24 m). He climbed into


id: list-of-rogue-waves-incidents-20260505-4
file: data/en.wikipedia.org/wiki/List_of_rogue_waves_incidents-4.md
category: reference
title: List of rogue waves incidents
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_rogue_waves_incidents
date_saved: 2026-05-05T08:18:17.503231+00:00
instance: kb-cron
parent: list-of-rogue-waves-incidents-20260505-0
summary:
=== 21st century === The Bahamian-registered cruise ships MS Bremen and MS Caledonian Star encountered 30-meter (98 ft) freak waves in the South Atlantic in 2001. Bridge windows on both ships were smashed, and all power and instrumentation lost. Naval Research Laboratory ocean-floor pressure sensors detected a freak wave caused by Hurricane Ivan in the Gulf of Mexico in 2004. The wave was around 27.7 meters (91 ft) high from peak to trough, and around 200 meters (660 ft) long. Norwegian Dawn, (three waves in succession, off the coast of Georgia, 16 April 2005): "The sea had actually calmed down when the 21-metre (69 ft) wave seemed to come out of thin air… Our captain, who has 20 years on the job, said he never saw anything like it." "The water exerted enough force to shear off the welds for the aluminum rail supports on the [ninth- and tenth-level] balconies of two cabins, allowing the teak balcony rails to break loose and crash into the cabin windows. The broken glass filling the drains compounded the water damage by allowing a large amount of water to enter the two cabins and damage the carpets in 61 other cabins. The ship's operating


id: list-of-meteorologists-20260505-0
file: data/en.wikipedia.org/wiki/List_of_meteorologists-0.md
category: reference
title: List of meteorologists
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_meteorologists
date_saved: 2026-05-05T08:18:18.835134+00:00
instance: kb-cron
parent: list-of-meteorologists-20260505-0
summary:
== A–B == Cleveland Abbe Aristotle June Bacon-Bercey David Bates Francis Beaufort Tor Bergeron Jacob Bjerknes Vilhelm Bjerknes Howard B. Bluestein Bert Bolin Léon Teisserenc de Bort Harold E. Brooks Keith Browning David Brunt C.H.D. Buys Ballot Horace R. Byers == C–D == Matthew Cappucci DaNa Carlis Jule Gregory Charney Coching Chu Isaac Cline Balfour Currie John Dalton Robert Davies-Jones William Morris Davis Igor Delijanić Jean-André Deluc Charles A. Doswell III Heinrich Wilhelm Dove == E–F == V. Walfrid Ekman Kerry Emanuel John Farrah William Ferrel Rich Fields John Park Finley Michael Fish Robert FitzRoy Bert Foord Benjamin Franklin Tetsuya Theodore Fujita == G–H == Francis Galton Audronė Galvonaitė Allison Göhler Ernest Gold William M. Gray Thomas P. Grazulis Willis Ray Gregg George Hadley Edmond Halley Julius von Hann Kenneth Hare Ingrid Holford Brian Hoskins Luke Howard == J–K == Robert Johns Jan-Erik Johnsen John Knox Wladimir Köppen Shen Kuo == L–O == Hubert Lamb Christopher Landsea Leslie R. Lemon Johannes Letzmann Richard Lindzen Mònica López Edward Norton Lorenz David M. Ludlum Paul Markowski Charles F. Marvin Cliff Mass Patrick McTaggart-Cowan Pomponius Mela Milutin Milanković James T. Moore Joel Myers Aili Nurminen Isidoro Orlanski == P–R == Erik Palmén Allen


id: list-of-meteorological-photos-and-videos-20260505-0
file: data/en.wikipedia.org/wiki/List_of_meteorological_photos_and_videos-0.md
category: reference
title: List of meteorological photos and videos
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_meteorological_photos_and_videos
date_saved: 2026-05-05T08:18:20.153817+00:00
instance: kb-cron
parent: list-of-meteorological-photos-and-videos-20260505-0
summary:
There are several notable photographs or videos in the field of meteorology, the study of the Earth's atmosphere, climate, and weather. These images or videos may be referred to as historic, most important, most iconic, or most influential weather-related photographs or weather-related videos. == List == === 19th century === === 20th century === === 21st century === == See also == List of photographs considered the most important == References ==


id: list-of-cat-documentaries-television-series-and-cartoons-20260505-0
file: data/en.wikipedia.org/wiki/List_of_cat_documentaries,_television_series_and_cartoons-0.md
category: reference
title: List of cat documentaries, television series and cartoons
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_cat_documentaries,_television_series_and_cartoons
date_saved: 2026-05-05T08:18:34.681061+00:00
instance: kb-cron
parent: list-of-cat-documentaries-television-series-and-cartoons-20260505-0
summary:
List of cat documentaries, television series and cartoons includes serious documentaries, television series and cartoons, in alphabetical order, related to cats . == Documentaries == Cat Empire: Docuseries (2021), Ubique Film Cats: Caressing the Tiger (1991), National Geographic Cats: Choosing, Caring and Training (2008), Revolution LLC Kedi (2016), Termite Films The Lion in Your Living Room (2015), Canadian Broadcasting Company Science of Cats (2014), National Geographic Secret Life of Cats (2014), National Geographic The Standard of Perfection: Show Cats (2009), Public Broadcasting Service Understanding Cats (2009), Public Broadcasting Service The World of Cats (2008), Columbia River Entertainment === Big cats documentaries === Big Cats (2018, 3 episodes), BBC Lions of Darkness (1993) National Geographic Lions of the African Night (1987) National Geographic Tiger King: Murder, Mayhem and Madness (2020, 7 episodes), Netflix === Documentary and reality series === Cats 101 (2009–2012), Animal Planet My Cat from Hell (2011–2016), Animal Planet Must Love Cats (2011–2012), Animal Planet == Cartoons == Garfield (1978–present; TV series 1988–1994, 2009–2016, 2019–2020), Universal Press Syndicate Heathcliff (1980–1981, 1984–1985), Ruby-Spears Productions, et al. The Itchy & Scratchy Show (1988–1997, as an element of The Simpsons), 20th Television Krazy Kat (1913–1944), King Features Syndicate The Ren and Stimpy


id: list-of-nature-conservation-organizations-20260505-0
file: data/en.wikipedia.org/wiki/List_of_nature_conservation_organizations-0.md
category: reference
title: List of nature conservation organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_nature_conservation_organizations
date_saved: 2026-05-05T08:18:36.001086+00:00
instance: kb-cron
parent: list-of-nature-conservation-organizations-20260505-0
summary:
This is a list of nature conservation organisations that primarily aim to protect species, their habitats, and ecosystems. == List of international conservation organisations == African Wildlife Foundation - ensuring that wildlife and wild lands thrive in modern Africa Bat Conservation International - working to conserve the world's bats and their habitats BirdLife International - a global partnership of organisations that strive to conserve birds Center for Biological Diversity - protecting endangered species through legal action, petitions, media and activism Conservation International - secure the critical benefits that nature provides to humanity Durrell Wildlife Conservation Trust - mission to save species from extinction EcoHealth Alliance - protecting the health of people, animals, and the environment from emerging infectious diseases Fauna and Flora International - safeguard the future of southern Africa's large mammal populations Greenpeace - raising environmental issues to public knowledge International Anti-Poaching Foundation - created a structured military-like approach to conservation in Africa International Union for Conservation of Nature - a partnership of 1400 organisations working in the field of nature conservation MarAlliance - non-profit that supports the effective management and conservation of large marine wildlife and their critical habitats with the support of dependent communities. National Audubon Society


id: index-of-conservation-articles-20260505-0
file: data/en.wikipedia.org/wiki/Index_of_conservation_articles-0.md
category: reference
title: Index of conservation articles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Index_of_conservation_articles
date_saved: 2026-05-05T08:18:37.189423+00:00
instance: kb-cron
parent: index-of-conservation-articles-20260505-0
summary:
This is an index of conservation topics. It is an alphabetical index of articles relating to conservation biology and conservation of the natural environment. == A == Abiotic stress - Adaptive management - Adventive plant - Aerial-seeding - Agreed Measures for the Conservation of Antarctic Fauna and Flora - Agroecology - American Prairie Foundation - Anti-whaling - Assisted migration - Assisted migration of forests in North America == B == Biodegradation - Biodiversity - Biodiversity action plan - Biodiversity hotspot - Biogenic - Biodiversity Outcomes Framework - Biogeographic realm - Biogeography - Bioinformatics - Biological integrity - Biomagnification - Biomaterial - Biome - Biomimicry - Biomonitoring - Biophilia hypothesis - Biophilic design - Biopiracy - Bioregion - Bioregionalism - Biosafety - Biosalinity - Biosecurity - Biosphere - Biosphere reserve - Biostatistics - Biosurvey - Biotechnology - Bioterrorism - Biotransference - Bird conservation - Blue-listed - Bottom trawling - Buffer zone == C == Captive breeding - Cave conservation - Charismatic megafauna - CITES - Common species - Community-based conservation - Compassionate conservation - Conference of Governors - Conservation agriculture - Conservation area - Conservation authority - Conservation biology - Conservation Commons - Conservation community - Conservation dependent - Conservation designation


id: natural-regions-of-germany-20260505-0
file: data/en.wikipedia.org/wiki/Natural_regions_of_Germany-0.md
category: reference
title: Natural regions of Germany
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Natural_regions_of_Germany
date_saved: 2026-05-05T08:18:38.455696+00:00
instance: kb-cron
parent: natural-regions-of-germany-20260505-0
summary:
This division of Germany into major natural regions takes account primarily of geomorphological, geological, hydrological, and pedological criteria in order to divide the country into large, physical units with a common geographical basis. Political boundaries play no part in this, apart from defining the national border. In addition to a division of Germany by natural regions, the federal authorities have also produced a division by so-called landscape areas (Landschaftsräume) that is based more on human utilisation of various regions and so has clearly different boundaries. == Groundwork by the Federal Institute of Regional Studies (BfL) == The natural region classification of Germany, as used today by the Federal Office for Nature Conservation (Bundesamt für Naturschutz or BfN) and by most state institutions, is largely based on the work in producing the Handbook of Natural Region Divisions of Germany between the years 1953 to 1962. This divided the present federal territory (then West and East Germany) into 86 so-called major landscape unit groups (Haupteinheitgruppen) each with a two-digit number between 01 and 90. These, in turn, were subdivided into up to ten, in some cases more, major landscape units (Haupteinheiten), each with a three-digit number. The handbook was accompanied by 1:100,000


id: natural-regions-of-germany-20260505-1
file: data/en.wikipedia.org/wiki/Natural_regions_of_Germany-1.md
category: reference
title: Natural regions of Germany
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Natural_regions_of_Germany
date_saved: 2026-05-05T08:18:38.455696+00:00
instance: kb-cron
parent: natural-regions-of-germany-20260505-0
summary:
The first version by Heinrich Müller-Miny appeared in the updated handbook map, the overview maps of the individual map sheets from 1960 and in the ninth edition of the handbook (1962) In the map sheets from publication year 1964 this version was slightly changed: The Upper Palatine-Upper Main Hills (Oberpfälzisch-Obermainische Hügelland) was raised from the third to the second level. The secondary landscape region of Lössbörden was expanded, especially in the west. There was another change in the map sheets from 1979 (Sheet 182 Burghausen) until their last publication (Sheet München and Tegernsee 1994): The primary landscape region, Central Uplands (Mittelgebirge), was divided in two into Mittelgebirgsschwelle and Schichtstufenland The classification of the Natural regions in Saxony, published after that of the Institute for Regional Studies and continually revised, allocates the larger northern part of the major unit group of Upper Lusatia (Oberlausitz) to the Lössbörden, so that only the Lusatian Mountains (Lausitzer Bergland) in the south remains within the Central Uplands. For clarity the first and second levels of the major landscape regions are organised from north to south and from west to east. Within a secondary or tertiary landscape region the list follows the numerical order in the


id: natural-regions-of-germany-20260505-2
file: data/en.wikipedia.org/wiki/Natural_regions_of_Germany-2.md
category: reference
title: Natural regions of Germany
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Natural_regions_of_Germany
date_saved: 2026-05-05T08:18:38.455696+00:00
instance: kb-cron
parent: natural-regions-of-germany-20260505-0
summary:
Upper Rhine Plain (D53) 23 Rhine-Main Basin 22 Northern Upper Rhine Plain 21 Middle Upper Rhine Plain 20 Southern Upper Rhine Plain ==== South German Scarplands ==== Source: (arranged by escarpments Grundgebirge/Buntsandstein, Muschelkalk, Keuper-Lias and Malm from north to south, internally from west to east. 14 Odenwald-Spessart-Rhön (D55) 15 Black Forest (D54) Swabian-Franconian Gäue 12 Neckar and Tauber Gäu Plateaus (D57) 13 Main Franconia Plateau (D56) Swabian-Franconian Keuper-Lias Lands 10 Swabian Keuper-Lias Lands (D58) 11 Franconian Keuper-Lias Lands (D59) Swabian-Franconian Jura 09 Swabian Jura (D60) 08 Franconian Jura (D61) 16 Upper Rhine Region (Dinkelberg and Upper Rhine Valley) (D69) ==== Upper Palatine-Upper Main Hills ==== 07 Upper Palatine-Upper Main Hills (D62) === Alpine Foreland === Source: arranged from north to south and from west to east) ==== Northern Alpine Foreland ==== 04 Iller-Lech Plateau (D64) Lower Bavarian Upland and Isar-Inn Gravel Plateau (D65) 06 Lower Bavarian Upland 05 Isar-Inn Gravel Plateau ==== Southern Alpine Foreland ==== Pre-Alpine Hills and Moorland (= Southern Alpine Foreland; D66) 03 Subalpine New Moraine Land 02* Nagelfluh Hills and Basins between Lake Constance and Wertach === Alps === The following 3 groups were still counted as part of (ex-)group 02 in the Handbook; the German


id: list-of-glaciers-20260505-0
file: data/en.wikipedia.org/wiki/List_of_glaciers-0.md
category: reference
title: List of glaciers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_glaciers
date_saved: 2026-05-05T08:18:39.696555+00:00
instance: kb-cron
parent: list-of-glaciers-20260505-0
summary:
A glacier (US: GLAY-shər) or (UK: ) is a persistent body of dense ice that is constantly moving under its own weight; it forms where the accumulation of snow exceeds its ablation (melting and sublimation) over many years, often centuries. Glaciers slowly deform and flow due to stresses induced by their weight, creating crevasses, seracs, and other distinguishing features. Because glacial mass is affected by long-term climate changes, e.g., precipitation, mean temperature, and cloud cover, glacial mass changes are considered among the most sensitive indicators of climate change. There are about 198,000 to 200,000 glaciers in the world. Catalogs of glaciers include: World Glacier Inventory World Glacier Monitoring Service Global Land Ice Measurements from Space (GLIMS) Glacier Database Randolph Glacier Inventory (RGI) == Glaciers by continent == === Africa === Africa, specifically East Africa, has contained glacial regions, possibly as far back as the last glacier maximum 10 to 15 thousand years ago. Seasonal snow does exist on the highest peaks of East Africa as well as in the Drakensberg Range of South Africa, the Stormberg Mountains, and the Atlas Mountains in Morocco. Currently, the only remaining glaciers on the continent exist on Mount Kilimanjaro, Mount Kenya, and the Rwenzori.


id: list-of-habitats-of-principal-importance-in-wales-20260505-0
file: data/en.wikipedia.org/wiki/List_of_habitats_of_principal_importance_in_Wales-0.md
category: reference
title: List of habitats of principal importance in Wales
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_habitats_of_principal_importance_in_Wales
date_saved: 2026-05-05T08:18:40.968477+00:00
instance: kb-cron
parent: list-of-habitats-of-principal-importance-in-wales-20260505-0
summary:
Wales is obliged by law to maintain lists of species and habitats of principal importance for biodiversity conservation; the other countries within the UK: Scotland, England and Northern Ireland, have their own laws for this purpose. Public bodies, including local authorities now have a legal duty to have regard to conserving biodiversity in the exercise of their normal functions. In Wales, that obligation originally derived from section 42 of the Natural Environment and Rural Communities (NERC) Act 2006. However, this requirement for Wales has since been superseded by an almost identical requirement enshrined within the Environment (Wales) Act 2016. == Selection == The habitats that have been designated to be of "principal importance for the purpose of conserving biodiversity" derive from lists originally drawn up for the UK Biodiversity Action Plan (UK BAP). These lists were reviewed in 2007, and the total number of UK BAP habitats increased from 45 to 65, and the number of UK BAP species increased from under 600 to 1,150. From these, the formal list just for Wales (and laid out below) now contains 53 of those 65 habitats. === Legal obligations === Section 6 of the Environment (Wales) Act 2016 places a legal obligation


id: list-of-herbaria-in-europe-20260505-0
file: data/en.wikipedia.org/wiki/List_of_herbaria_in_Europe-0.md
category: reference
title: List of herbaria in Europe
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_herbaria_in_Europe
date_saved: 2026-05-05T08:18:42.184594+00:00
instance: kb-cron
parent: list-of-herbaria-in-europe-20260505-0
summary:
This is a list of herbaria in Europe, organized first by region where the herbarium is located (using the United Nations geoscheme for Europe), then within each region by size of the collection. For other continents, see List of herbaria. == Eastern Europe == The tables below list herbaria located in Eastern Europe as defined by the United Nations geoscheme for Europe. === Black Sea === The following table includes herbaria located in countries on the Black Sea, including Bulgaria, Moldova, Romania, and Ukraine. === Czech Republic === The following table includes herbaria located in the Czech Republic. === Hungary === The following table includes herbaria located in Hungary. === Poland === The following table includes herbaria located in Poland. === Russia === The following table includes herbaria located in European Russia. === Ukraine === National Herbarium of Ukraine (KW) == Northern Europe == The tables below list herbaria located in Northern Europe as defined by the United Nations geoscheme for Europe: Ireland, the British Isles, Baltic states, Scandinavia, and Iceland. === Baltic states === The following table includes herbaria located in the Baltic states: Estonia, Latvia, and Lithuania. === Britain & Ireland === The following table includes herbaria located


id: list-of-herbaria-in-north-america-20260505-0
file: data/en.wikipedia.org/wiki/List_of_herbaria_in_North_America-0.md
category: reference
title: List of herbaria in North America
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_herbaria_in_North_America
date_saved: 2026-05-05T08:18:43.376729+00:00
instance: kb-cron
parent: list-of-herbaria-in-north-america-20260505-0
summary:
This is a list of herbaria in North America, organized first by country or region where the herbarium is located, then within each region by size of the collection. All herbarium codes follow the Index Herbariorum. For other continents, see List of herbaria. == Canada == == Central America and the Caribbean == The table below lists herbaria located in Central America and the Caribbean. == Mexico == == United States == == References ==


id: list-of-herbaria-in-turkey-20260505-0
file: data/en.wikipedia.org/wiki/List_of_herbaria_in_Turkey-0.md
category: reference
title: List of herbaria in Turkey
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_herbaria_in_Turkey
date_saved: 2026-05-05T08:18:44.619963+00:00
instance: kb-cron
parent: list-of-herbaria-in-turkey-20260505-0
summary:
The following is a list of herbaria in Turkey. Herbaria are established within faculties and institutes of credible universities. Those created in departments that are concerned with natural sciences such as botany, ecology, biogeography and climatology are mostly used to do research on the genetics of the plants, to examine their distribution on specific geographical locations and to protect them for future generations, while those affiliated with more practice-based departments such as pharmacy are used as a resource for drug production techniques. The first herbarium in Turkey was opened in 1933 within the Faculty of Science at Ankara University. Founded by Kurt Krause and Hikmet Birand, this herbarium is the oldest among its counterparts in the country and has the most number of species within its 200,000-piece collection. Therefore, it is also called Herbarium Turcicum (Turkish Herbarium). The Sugar Institute Herbarium, Atatürk University Faculty of Science Herbarium and Ege University Faculty of Pharmacy Herbarium are closed to visitors and scientific researchers. However, thanks to a specially created website, it is possible to access all the data related to the Ege University Faculty of Pharmacy Herbarium remotely. Altınbaş University Faculty of Pharmacy Herbarium, which opened in 2018, is the first herbarium


id: list-of-herbaria-20260505-0
file: data/en.wikipedia.org/wiki/List_of_herbaria-0.md
category: reference
title: List of herbaria
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_herbaria
date_saved: 2026-05-05T08:18:45.907753+00:00
instance: kb-cron
parent: list-of-herbaria-20260505-0
summary:
This is a list of active herbaria, organized first by continent where the herbarium is located, then within each continent by size of the collection. The list is based on the Index Herbariorum, a global directory of herbaria and their associated staff. == Background == A herbarium (plural "herbaria") is a collection of preserved plant specimens. These specimens may be whole plants or plant parts: these will usually be in a dried form, mounted on a sheet, but depending upon the material may also be kept in alcohol or other preservative. The same term is often used in mycology to describe an equivalent collection of preserved fungi and in phycology to describe a collection of algae. To preserve their form and color, plants collected in the field are spread flat on sheets of newsprint and dried, usually in a plant press, between blotters or absorbent paper. The specimens, which are then mounted on sheets of stiff white paper, are labeled with all essential data, such as collector, date and place found, description of the plant, elevation, and special habitat conditions. The sheet is then placed in a protective case. As a precaution against insect damage, the pressed plant is frozen


id: iucn-protected-area-categories-20260505-0
file: data/en.wikipedia.org/wiki/IUCN_protected_area_categories-0.md
category: reference
title: IUCN protected area categories
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IUCN_protected_area_categories
date_saved: 2026-05-05T08:18:47.158801+00:00
instance: kb-cron
parent: iucn-protected-area-categories-20260505-0
summary:
IUCN protected area categories, or IUCN protected area management categories, are categories used to classify protected areas in a system developed by the International Union for Conservation of Nature (IUCN). The enlisting of such areas is part of a strategy being used toward the conservation of the world's natural environment and biodiversity. The IUCN has developed the protected area management categories system to define, record and classify the wide variety of specific aims and concerns when categorising protected areas and their objectives. Further supplementary guidelines have been developed specific to marine protected areas (MPAs). This categorisation method is recognised on a global scale by national governments and international bodies such as the United Nations and the Convention on Biological Diversity. == Categories == === Category I === ==== Category Ia – strict nature reserve ==== A strict nature reserve (IUCN Category Ia) is an area which is protected from all but light human use in order to protect its biodiversity and also possibly its geological/geomorphological features. These areas are often home to dense native ecosystems where all human disturbance except scientific study, environmental monitoring and education is prohibited. Because these areas are so strictly protected, they provide ideal pristine environments


id: iucn-protected-area-categories-20260505-1
file: data/en.wikipedia.org/wiki/IUCN_protected_area_categories-1.md
category: reference
title: IUCN protected area categories
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IUCN_protected_area_categories
date_saved: 2026-05-05T08:18:47.158801+00:00
instance: kb-cron
parent: iucn-protected-area-categories-20260505-0
summary:
=== Category V – protected landscape or seascape === A protected landscape or protected seascape (IUCN Category V) covers a body of land or ocean with an explicit natural conservation plan, but usually also accommodates a range of for-profit activities. The main objective is to safeguard regions that have built up a distinct and valuable ecological, biological, cultural, or scenic character. In contrast with previous categories, Category V permits surrounding communities to interact more with the area, contributing to the area's sustainable management and engaging with its natural and cultural heritage. Landscapes and seascapes that fall into this category should represent an integral balance between people and nature and can sustain activities such as traditional agricultural and forestry systems on conditions that ensure the continued protection or ecological restoration of the area. Category V is one of the more flexible classifications of protected areas. As a result, protected landscapes and seascapes may be able to accommodate contemporary developments, such as ecotourism, at the same time as maintaining the historical management practices that may procure the sustainability of agrobiodiversity and aquatic biodiversity. === Category VI – protected area with sustainable use of natural resources === Though human involvement is a large


id: list-of-animals-by-number-of-legs-20260505-0
file: data/en.wikipedia.org/wiki/List_of_animals_by_number_of_legs-0.md
category: reference
title: List of animals by number of legs
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_animals_by_number_of_legs
date_saved: 2026-05-05T08:18:48.428358+00:00
instance: kb-cron
parent: list-of-animals-by-number-of-legs-20260505-0
summary:
The following is a list of selected animals in order of increasing number of legs, from 0 legs to 653 pairs of legs, the maximum recorded in the animal kingdom. Each entry provides the relevant taxa up to the rank of phylum. Each entry also provides the common name of the animal. If the relevant taxon includes different animals with different common names, then the entry provides the common name of a familiar example. If juveniles have fewer legs than adults, then the animal is listed by the number of legs recorded in mature adults. If this number varies among adults within the taxon, then this variation is noted in a comment. In counting legs, this list follows conventions adopted in the relevant literature. For example, millipedes with gonopods are listed by numbers that exclude leg pairs that become gonopods, but numbers for millipedes with telopods include leg pairs that become telopods. Animals have been selected so that each number from 0 to 55 leg pairs has one example listed. Each of these examples is listed by a number closely associated with the relevant taxon, either because that number is the one most commonly observed in that taxon or because


id: list-of-long-distance-footpaths-20260505-0
file: data/en.wikipedia.org/wiki/List_of_long-distance_footpaths-0.md
category: reference
title: List of long-distance footpaths
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_long-distance_footpaths
date_saved: 2026-05-05T08:18:49.672015+00:00
instance: kb-cron
parent: list-of-long-distance-footpaths-20260505-0
summary:
This is a list of some long-distance footpaths used for walking and hiking. == Africa == === Lesotho === 3 Ranges Trail: 288.3 km (179.1 mi) a hiking trail that passes three mountain ranges, namely Thaba Putsoa Range, Central Range and ends at Drakensburg Range. It starts at Lesotho lowest point, at the confluence of Makhaleng and Senqu and ends at the country's highest point, Thabana Ntlenyane (3482m). === Namibia === Fish River Canyon: 90 km (56 mi) route in the ǀAi-ǀAis/Richtersveld Transfrontier Park === South Africa === Otter Trail: 44 km (27 mi) section of the Garden Route along the Cape coast Drakensberg Grand Traverse: rugged 205 km (127 mi) trek in KwaZulu-Natal === Egypt === Sinai Trail: 250 km (160 mi) thru-hike from Nuweiba to Mount Catherine === Uganda === Sir Samuel and Lady Florence Baker Trail: 575 km (357 mi) trek through northern Uganda == Asia == === Bangladesh === Jhiri Path: ascent of Keokradong, one of the highest mountains in Bangladesh. === Bhutan === Snowman Trek: 328 km (204 mi) trek through high passes near the border with Tibet [1] === Hong Kong === Hong Kong Trail: 50 km (31 mi) across Hong Kong Island Lantau


id: list-of-long-distance-footpaths-20260505-1
file: data/en.wikipedia.org/wiki/List_of_long-distance_footpaths-1.md
category: reference
title: List of long-distance footpaths
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_long-distance_footpaths
date_saved: 2026-05-05T08:18:49.672015+00:00
instance: kb-cron
parent: list-of-long-distance-footpaths-20260505-0
summary:
=== Türkiye === Sufi Trail – 801 km (498 mi) trail from Istanbul to Konya, following the Ottoman Sultans Hajj route Lycian Way – 540 km (340 mi) trail around the south coast of Turkey Saint Paul Trail – 500 km (310 mi) trail following St Paul's 1st journey Sultans Trail runs 2,200 km (1,400 mi) from Vienna through the Balkans, terminating in Istanbul Kaçkar Trails – 8 multi-day trails in Northeast Turkey Evliya Çelebi Way – the first part of Evliya's route to Mecca in the 17th century Phrygian Way – three separate trekking and cycling trails of total 506 km (314 mi) in the Phrygian Valleys, western Turkey,[2] Carian Trail – 800 km (500 mi) hugging the south-west coast of Turkey == Europe == Some of the best known footpaths in Europe are joined by 12 designated European long-distance paths over some 70,000 km (43,000 mi). Some other popular international routes include: GR (Grande Randonnée) footpaths in Belgium, France, Spain and the Netherlands Tour du Mont Blanc, circling the Mont Blanc massif in Italy, Switzerland, and France. It covers a distance of roughly 170 km (110 mi) with 10 km (6.2 mi) of elevation change. Haute Randonnée Pyrénéenne


id: list-of-long-distance-footpaths-20260505-2
file: data/en.wikipedia.org/wiki/List_of_long-distance_footpaths-2.md
category: reference
title: List of long-distance footpaths
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_long-distance_footpaths
date_saved: 2026-05-05T08:18:49.672015+00:00
instance: kb-cron
parent: list-of-long-distance-footpaths-20260505-0
summary:
Barbarossaweg: Korbach to Kyffhäuserdenkmal (332 km (206 mi)) Bergischer Weg: Essen to Königswinter (137 km (85 mi)) Birkenhainer Strasse: Hanau to Gemünden am Main (71 km (44 mi)) Bonifatiusweg: Mainz to Fulda (180 km (110 mi)) Christine-Koch-Weg: Menden to Bad Laasphe (123 km (76 mi)) Eselsweg: Schlüchtern to Großheubach (111 km (69 mi)) König-Ludwig-Weg: Berg am Starnberger See to Füssen (120 km (75 mi)) Maximiliansweg: Lindau to Berchtesgaden (350 km (220 mi)) Moselhöhenweg: Trier to Koblenz Pandurensteig: Waldmuenchen to Passau Rennsteig: Hörsel to Blankenstein/Saale through the Thuringian Forest (169 km (105 mi)) Rheinburgenweg Trail: Bingen to Koblenz to Rüdesheim am Rhein (c.200 km (120 mi)) Rheinhöhenweg Trail: Bonn to Alsheim/Wiesbaden (530 km (330 mi)) Rheinsteig: Bonn to Wiesbaden (320 km (200 mi)) Westweg (Black Forest western ridgeway): Pforzheim to Basel (279 km (173 mi)) Mittelweg (Black Forest central ridgeway): Pforzheim to Waldshut (233 km (145 mi)) Ostweg (Black Forest eastern ridgeway): Pforzheim to Schaffhausen (238 km (148 mi)) Black Forest North Perimeter Way: Mühlacker to Karlsruhe (71 km (44 mi)) Two Valleys Trail: round hiking trail from/to Waldkirch (106 km (66 mi)) Freiburg-Lake Constance Black Forest Trail: Freiburg to Konstanz (183 km (114 mi)) Saar-Hunsrück-Steig: Trier to Saarschleife in Mettlach


id: list-of-long-distance-footpaths-20260505-3
file: data/en.wikipedia.org/wiki/List_of_long-distance_footpaths-3.md
category: reference
title: List of long-distance footpaths
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_long-distance_footpaths
date_saved: 2026-05-05T08:18:49.672015+00:00
instance: kb-cron
parent: list-of-long-distance-footpaths-20260505-0
summary:
=== Serbia === The Fruška Gora Transversal (Serbian: Fruškogorska Transverzala) – circular trail around Fruška Gora mountain – 160 km (100 mi) The Small Toplica Transversal (Serbian: Mala Toplička Transverzala) – 122 km (76 mi) === Slovakia === The SNP Heroes Trail, 770 km (480 mi) from Dukla Pass to Devín, across mountainous regions of Slovakia === Slovenia === Slovenian Mountain Hiking Trail 599 km (372 mi) from east (Maribor) to west (Ankaran) === Spain === Way of St. James (Spanish: El Camino de Santiago) Route of the Monasteries of Valencia (Spanish: Ruta de los Monasterios de Valencia) Grande Randonnée 7 (GR 7): From Tarifa to the mountain cabin of Fontferrera, part of the E4 route. Grande Randonnée 11 (GR 11): Pyrenees Trail, staying within Spain. Haute Randonnée Pyrénéenne (HRP): High Pyrenees Trail, along the border with France. Way of the Lighthouses: 200 km (120 mi) along the coastline from Malpica to Fisterra, in Galicia (Spain) === Sweden === Kungsleden, 425 km (264 mi) from the northern extremity of the country Sörmlandsleden 1,000 km (620 mi) of winding paths through the county of Sörmland. Bohusleden 360 km (220 mi) past at Göteborg, Uddevalla, Munkedal and ends finally in Strömstad Ingegerdsleden,


id: list-of-long-distance-footpaths-20260505-4
file: data/en.wikipedia.org/wiki/List_of_long-distance_footpaths-4.md
category: reference
title: List of long-distance footpaths
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_long-distance_footpaths
date_saved: 2026-05-05T08:18:49.672015+00:00
instance: kb-cron
parent: list-of-long-distance-footpaths-20260505-0
summary:
=== Brazil === Atlantic Forest Trail 4,270 km (2,400 mi) follows the Serra do Mar mountain range, crossing five Brazilian States and connecting 10 national parks, and many historical trails and traditional communities. (very hard trail) Transmantiqueira Trail 1,200 km (750 mi) crosses the Mantiqueira range in a west–east direction (very hard trail) Petrópolis Teresópolis Traverse 36 km (22 mi) between Petrópolis and Teresópolis (medium to hard trail) Transcarioca Trail 183 km (114 mi) in Rio de Janeiro city (medium to hard trail) Caminho da Fé 538 km (334 mi). There are 3 different starting points: from Sao Carlos to Aparecida, São Paulo or from Cravinhos to Aparecida or from Mococa to Aparecida === Costa Rica === 280 km from Atlantic to Pacific coasts of Costa Rica El Camino de Costa Rica === Chile === Central Chile and Patagonia 3,000 km (1,900 mi) Greater Patagonian Trail from the capital Santiago de Chile to the Southern Patagonian Ice Field. Magallanes 118 km (73 mi). Full circuit of Torres del Paine, including Valle del Francés and access to the base of Torres del Paine. Dientes de Navarino Circuit ≈53 km (33 mi). 3‑7 days. Starts out of Puerto Williams. Access from mainland


id: list-of-national-wildlife-refuges-established-for-endangered-species-20260505-0
category: reference
title: List of National Wildlife Refuges established for endangered species
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_National_Wildlife_Refuges_established_for_endangered_species
date_saved: 2026-05-05T08:18:52.021938+00:00
instance: kb-cron
parent: list-of-national-wildlife-refuges-established-for-endangered-species-20260505-0
file:
data/en.wikipedia.org/wiki/List_of_National_Wildlife_Refuges_established_for_endangered_species-0.md

summary:
This is a list of National Wildlife Refuges established specifically for the protection of one or more endangered species on the United States Fish and Wildlife Service list of endangered mammals and birds. == References ==


id: list-of-natural-phenomena-20260505-0
file: data/en.wikipedia.org/wiki/List_of_natural_phenomena-0.md
category: reference
title: List of natural phenomena
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_natural_phenomena
date_saved: 2026-05-05T08:18:54.736426+00:00
instance: kb-cron
parent: list-of-natural-phenomena-20260505-0
summary:
A natural phenomenon is an observable event which is not man-made. Examples include: sunrise, weather, fog, thunder, tornadoes; biological processes, decomposition, germination; physical processes, wave propagation, erosion; tidal flow, and natural disasters such as electromagnetic pulses, volcanic eruptions, hurricanes and earthquakes. == History == Over many intervals of time, natural phenomena have been observed by a series of countless events as a feature created by nature. == Physical phenomena == The act of: Freezing Boiling Gravity Magnetism === Gallery === == Chemical phenomena == Oxidation Fire Rusting == Biological phenomena == Metabolism Catabolism Anabolism Decomposition – by which organic substances are broken down into a much simpler form of matter Fermentation – converts sugar to acids, gases and/or alcohol. Growth Birth Death Population decrease === Gallery === == Astronomical phenomena == Supernova Gamma ray bursts Quasars Blazars Pulsars Cosmic microwave background radiation == Geological phenomena == Mineralogic phenomena Lithologic phenomena Rock types Igneous rock Igneous formation processes Sedimentary rock Sedimentary formation processes (sedimentation) Quicksand Metamorphic rock Endogenic phenomena Plate tectonics Continental drift Earthquake Oceanic trench Phenomena associated with igneous activity Geysers and hot springs Bradyseism Volcanic eruption Earth's magnetic field Exogenic phenomena Slope phenomena Slump Landslide Weathering phenomena Erosion Glacial


id: list-of-common-household-pests-20260505-0
file: data/en.wikipedia.org/wiki/List_of_common_household_pests-0.md
category: reference
title: List of common household pests
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_common_household_pests
date_saved: 2026-05-05T08:18:56.020269+00:00
instance: kb-cron
parent: list-of-common-household-pests-20260505-0
summary:
This is a list of common household pests – undesired animals that have a history of living, invading, causing damage, eating human foods, acting as disease vectors or causing other harms in human habitation. == Mammals == Mice Field mice House mice Possums Brushtail possum Ringtail possum Rats Black rats Brown rats Wood rats Cotton rats == Invertebrates == Ants Argentine ants Carpenter ants Fire ants Odorous house ants Pharaoh ants Thief ants Bed bugs Beetles Woodworms Death watch beetles Furniture beetles Weevils Maize weevil Rice weevil Carpet beetles Fur beetles Varied carpet beetles Spider beetles Mealworm beetles Centipedes House centipedes Cockroaches Brown-banded cockroaches German cockroaches American cockroaches Oriental cockroaches Dust mites Earwigs Crickets House crickets Firebrats Flies Bottle flies Blue bottle flies Green bottle flies House flies Fruit flies Drain flies Phorid flies Gnats (Fungus gnats) Mosquitoes Moths Almond moths Indianmeal moths Clothes moths Common clothes moths Brown house moths Paper Lice Red spiders Silverfish Spiders Termites Dampwood termites Subterranean termites Woodlouse == See also == Home-stored product entomology List of notifiable diseases Noxious weed Pest (organism) == References ==


id: outline-of-the-cascade-range-20260505-0
file: data/en.wikipedia.org/wiki/Outline_of_the_Cascade_Range-0.md
category: reference
title: Outline of the Cascade Range
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Outline_of_the_Cascade_Range
date_saved: 2026-05-05T08:18:57.324967+00:00
instance: kb-cron
parent: outline-of-the-cascade-range-20260505-0
summary:
The following outline is provided as an overview of and topical guide to the Cascade Range: The Cascade Range, or Cascades, is a major mountain range of western North America, extending from southern British Columbia through Washington and Oregon to Northern California. It includes both non-volcanic mountains, such as many of those in the North Cascades, and the notable volcanoes known as the High Cascades. The small part of the range in British Columbia is referred to as the Canadian Cascades or, locally, as the Cascade Mountains. The highest peak in the range is Mount Rainier in Washington at 14,411 feet (4,392 m). The Cascades are part of the Pacific Ocean's Ring of Fire, the ring of volcanoes and associated mountains around the Pacific Ocean. All of the eruptions in the contiguous United States over the last 200 years have been from the Cascade Volcanoes. The two most recent were Lassen Peak from 1914 to 1921 and a major eruption of Mount St. Helens in 1980. Minor eruptions of Mount St. Helens have also occurred since, most recently from 2004 to 2008. The Cascade Range is a part of the American Cordillera, a nearly continuous chain of mountain ranges (cordillera)


id: outline-of-the-cascade-range-20260505-1
file: data/en.wikipedia.org/wiki/Outline_of_the_Cascade_Range-1.md
category: reference
title: Outline of the Cascade Range
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Outline_of_the_Cascade_Range
date_saved: 2026-05-05T08:18:57.324967+00:00
instance: kb-cron
parent: outline-of-the-cascade-range-20260505-0
summary:
=== National parks === Lassen Volcanic National Park was established in 1916 while its namesake peak was erupting. The park includes the most extensive and active thermal areas in the United States outside Yellowstone National Park. Crater Lake National Park preserves the remains of Mount Mazama, a large volcano that imploded thousands of years ago, forming a caldera that was later filled with rain and ground water, later to be known as Crater Lake. Mount Rainier National Park surrounds the Cascades' highest volcano, Mount Rainier, which in turn is covered by the largest glacier system in the United States south of Alaska. North Cascades National Park was carved out of a primitive part of the range composed of ancient metamorphic and sedimentary rock. Mount Baker and Glacier Peak are nearby. === National Scenic Areas === Columbia River Gorge National Scenic Area === National monuments === Mount St. Helens National Volcanic Monument was formed following the 1980 eruption of Mount St. Helens in order to preserve the devastated area and give scientists a chance to study its recovery. Newberry National Volcanic Monument includes the area around Newberry Volcano in central Oregon. Cascade–Siskiyou National Monument is located in southern Oregon at the


id: new-7-wonders-of-nature-20260505-0
file: data/en.wikipedia.org/wiki/New_7_Wonders_of_Nature-0.md
category: reference
title: New 7 Wonders of Nature
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/New_7_Wonders_of_Nature
date_saved: 2026-05-05T08:18:58.591022+00:00
instance: kb-cron
parent: new-7-wonders-of-nature-20260505-0
summary:
New 7 Wonders of Nature (2007–2011) was an initiative started in 2007 to create a list of seven natural wonders chosen by people through a global poll. It was the second in a series of Internet-based polls led by Swiss-born Canadian Bernard Weber and organized by the New 7 Wonders Foundation a Swiss-based foundation which Weber founded. The initiative followed an earlier New 7 Wonders of the World campaign and attracted 100 million votes from around the world before voting finished on November 11, 2011. == Stages of the campaign == The New 7 Wonders of Nature campaign started in 2007, immediately after the campaign to elect the man-made New 7 Wonders of the World, in which more than 100 million votes were cast. From over 440 participants representing over 220 countries and through a national qualification and race to become one of the Top 77, as well as the recommendations of the Panel of Experts led by Prof. Federico Mayor, the list of 28 "Official Finalist Candidates" was determined. Voting until November 2011, during which time the New 7 Wonders World Tour planned to visit each of the finalists to allow them to present themselves to the voters across


id: list-of-parasitic-organisms-20260505-0
file: data/en.wikipedia.org/wiki/List_of_parasitic_organisms-0.md
category: reference
title: List of parasitic organisms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_parasitic_organisms
date_saved: 2026-05-05T08:18:59.799352+00:00
instance: kb-cron
parent: list-of-parasitic-organisms-20260505-0
summary:
This is an incomplete list of organisms that are true parasites upon other organisms. == Endoparasites == (endo = within; parasites that live inside their hosts) === Plants === Rafflesia Cuscuta Mistletoe === Parasitic worms === These can be categorized into three groups; cestodes, nematodes and trematodes. Examples include: Acanthocephala Ascariasis (roundworms) Cestoda (tapeworms) including: Taenia saginata (human beef tapeworm), Taenia solium (human pork tapeworm), Diphyllobothrium latum (fish tapeworm) and Echinococcosis (hydatid tapeworm) Clonorchis sinensis (the Chinese liver fluke) Dracunculus medinensis (Guinea worm) Enterobius vermicularis (pinworm) Filariasis Hookworm Loa loa Onchocerciasis (river blindness) Schistosomiasis Strongyloides stercoralis Tapeworm Toxocara canis (dog roundworm) Trichinella Whipworm === Protozoans === Entamoeba histolytica and Entamoeba coli - can cause Amoebiasis Acanthamoeba Balamuthia mandrillaris Giardia Cyclospora cayetanensis Cryptosporidium Toxoplasma gondii Leishmania - L. tropica, L. donovani, and L. mexicana are known to cause Leishmaniasis. Plasmodium - causes the fatal disease, Malaria. P. falciparum, P. vivax, and P. malariae are pathogenic to humans. Babesia === Fungi === Gymnosporangium and other rusts Pyrenophora teres Cordyceps === Arthropods === Pentastomida == Ectoparasites == (ecto = outside; parasites that live on but not within their hosts, for example, attached to their skin) === Arthropoda === Acari Varroa destructor Cymothoa exigua


id: list-of-pine-barrens-20260505-0
file: data/en.wikipedia.org/wiki/List_of_pine_barrens-0.md
category: reference
title: List of pine barrens
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_pine_barrens
date_saved: 2026-05-05T08:19:01.262537+00:00
instance: kb-cron
parent: list-of-pine-barrens-20260505-0
summary:
The following is a list of pine barrens. Canada Kaladar Jack Pine Barrens in Ontario United States Kentucky Hi Lewis Pine Barrens State Nature Preserve Maine Waterboro Barrens Preserve Hollis Plains Massachusetts Plymouth Pinelands Michigan Huron National Forest New Hampshire Ossipee Pine Barrens Concord Pine Barrens New Jersey Pine Barrens New York Albany Pine Bush Altona Flat Rock Jack Pine Barrens Long Island Central Pine Barrens Rome Sand Plains Shawangunk Ridge Pennsylvania Long Pond Barrens Scotia Barrens Rhode Island Kingston Pine Barrens West Virginia North Fork Mountain Wisconsin Great Lakes Barrens Moquah Barrens Research Natural Area Northwest Wisconsin Pine Barrens Gotham Jack Pine Barrens Spread Eagle Barrens Virginia Zuni Pine Barrens


id: seven-natural-wonders-20260505-0
file: data/en.wikipedia.org/wiki/Seven_Natural_Wonders-0.md
category: reference
title: Seven Natural Wonders
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Seven_Natural_Wonders
date_saved: 2026-05-05T08:19:03.022217+00:00
instance: kb-cron
parent: seven-natural-wonders-20260505-0
summary:
Seven Natural Wonders is a television series that was broadcast on BBC Two from 3 May to 20 June 2005. The programme takes an area of England each week and, from votes by the people living in that area, shows the 'seven natural wonders' of that area in a programme. == Episodes and locations == The series covered eight regions of England, having originated as a 'local' television project. There was also a series, looking at a similar selection of 'man-made' wonders for each of eleven regions of England. == References == == External links == Seven Natural Wonders at BBC Online


id: seven-natural-wonders-of-africa-20260505-0
file: data/en.wikipedia.org/wiki/Seven_Natural_Wonders_of_Africa-0.md
category: reference
title: Seven Natural Wonders of Africa
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Seven_Natural_Wonders_of_Africa
date_saved: 2026-05-05T08:19:04.178354+00:00
instance: kb-cron
parent: seven-natural-wonders-of-africa-20260505-0
summary:
The Seven Natural Wonders of Africa was a competition where the seven were selected by voting on February 11, 2013. == Seven Wonders of Africa == == See also == Wonders of the World (disambiguation) Wonders of the World == References ==


id: list-of-the-seven-natural-wonders-of-georgia-u-s-state-20260505-0
file: data/en.wikipedia.org/wiki/List_of_the_seven_natural_wonders_of_Georgia_(U.S._state)-0.md
category: reference
title: List of the seven natural wonders of Georgia (U.S. state)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_the_seven_natural_wonders_of_Georgia_(U.S._state)
date_saved: 2026-05-05T08:19:05.357691+00:00
instance: kb-cron
parent: list-of-the-seven-natural-wonders-of-georgia-u-s-state-20260505-0
summary:
The Seven Natural Wonders of Georgia are considered to be: Amicalola Falls Okefenokee Swamp Providence Canyon Radium Springs Stone Mountain Tallulah Gorge Warm Springs The first list of natural wonders was compiled by state librarian Ella May Thornton and published in the Atlanta Georgian magazine on December 26, 1926. That first list included: Amicalola Falls Jekyll Island Forest Marble vein in Longswamp Valley in Pickens County Okefenokee Swamp Stone Mountain Tallulah Gorge Warm Springs == References == == External links == Georgia Encyclopedia


id: seven-wonders-of-canada-20260505-0
file: data/en.wikipedia.org/wiki/Seven_Wonders_of_Canada-0.md
category: reference
title: Seven Wonders of Canada
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Seven_Wonders_of_Canada
date_saved: 2026-05-05T08:19:06.576406+00:00
instance: kb-cron
parent: seven-wonders-of-canada-20260505-0
summary:
The Seven Wonders of Canada was a 2007 competition sponsored by CBC Television's The National and CBC Radio One's Sounds Like Canada. They sought to determine Canada's "seven wonders" by receiving nominations from viewers, and then from on-line voting of the short list. After the vote, a panel of judges, Ra McGuire, Roy MacGregor and Roberta L. Jamieson, picked the winners based on geographic and poetic criteria. Their seven picks were revealed on The National on June 7, 2007, making the official Seven Wonders of Canada, the Canoe, the Igloo, Niagara Falls, Old Quebec City, Pier 21 Halifax, Prairie Skies, and the Rockies. CBC anchor Peter Mansbridge commented on the top winner, “it’s hard to imagine Canada being Canada without the canoe. Explorers, missionaries, fur traders and First Nations—they’re all linked by this subtle and simple craft. To many, the quintessential Canadian experience begins by picking up a paddle. That’s why the canoe is one of the seven wonders” (Osler 2014). There were over 25,000 nominations and 1 million votes cast, according to the CBC website. The top audience votes were the Sleeping Giant, Niagara Falls, the Bay of Fundy, Nahanni National Park Reserve, the Northern Lights, the Rockies, and


id: list-of-numbers-20260505-0
file: data/en.wikipedia.org/wiki/List_of_numbers-0.md
category: reference
title: List of numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_numbers
date_saved: 2026-05-05T08:19:08.279774+00:00
instance: kb-cron
parent: list-of-numbers-20260505-0
summary:
This is a list of notable numbers and articles about them. The list does not contain all numbers in existence as most of the number sets are infinite. Numbers may be included in the list based on their mathematical, historical or cultural notability, but all numbers have qualities that could arguably make them notable. Even the smallest "uninteresting" number is paradoxically interesting for that very property. This is known as the interesting number paradox. The definition of what is classed as a number is rather diffuse and based on historical distinctions. For example, the pair of numbers (3,4) is commonly regarded as a number when it is in the form of a complex number (3+4i), but not when it is in the form of a vector (3,4). This list will also be categorized with the standard convention of types of numbers. This list focuses on numbers as mathematical objects and is not a list of numerals, which are linguistic devices: nouns, adjectives, or adverbs that designate numbers. The distinction is drawn between the number five (an abstract object equal to 2+3), and the numeral five (the noun referring to the number). == Natural numbers == Natural numbers are a subset


id: list-of-numbers-20260505-1
file: data/en.wikipedia.org/wiki/List_of_numbers-1.md
category: reference
title: List of numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_numbers
date_saved: 2026-05-05T08:19:08.279774+00:00
instance: kb-cron
parent: list-of-numbers-20260505-0
summary:
A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is trivially a rational number. The set of all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a boldface Q (or blackboard bold Q {\displaystyle \mathbb {Q} } , Unicode U+211A ℚ DOUBLE-STRUCK CAPITAL Q); it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian for "quotient". Rational numbers such as 0.12 can be represented in infinitely many ways, e.g. zero-point-one-two (0.12), three twenty-fifths (⁠3/25⁠), nine seventy-fifths (⁠9/75⁠), etc. This can be mitigated by representing rational numbers in a canonical form as an irreducible fraction. A list of rational numbers is shown below. The names of fractions can be found at numeral (linguistics). == Real numbers == Real numbers are least upper bounds of sets of rational numbers that are bounded above, or greatest lower bounds of sets of rational numbers that are bounded below, or limits of convergent sequences of rational numbers. Real numbers that are not


id: list-of-group-0-isbn-publisher-codes-20260505-0
file: data/en.wikipedia.org/wiki/List_of_group-0_ISBN_publisher_codes-0.md
category: reference
title: List of group-0 ISBN publisher codes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_group-0_ISBN_publisher_codes
date_saved: 2026-05-05T08:19:09.633484+00:00
instance: kb-cron
parent: list-of-group-0-isbn-publisher-codes-20260505-0
summary:
A list of publisher codes for (978) International Standard Book Numbers with a group code of zero. == Assignment == The group-0 publisher codes are assigned as follows: == 2-digit publisher codes == == 3-digit publisher codes == (Note: the status of codes not listed in this table is unclear; please help fill the gaps.) == 4-digit publisher codes == (Note: many codes are not yet listed in this table; please help fill the gaps.) == 5-digit publisher codes == (Note: many codes are not yet listed in this table; please help fill the gaps.) == 6-digit publisher codes == (Note: many codes are not yet listed in this table; please help fill the gaps.) == 7-digit publisher codes == (Note: many codes are not yet listed in this table; please help fill the gaps.) == See also == List of group-1 ISBN publisher codes List of ISBN identifier groups == References == == External links == https://www.isbn-international.org/range_file_generation http://www.books-by-isbn.com/ List of 2 and 3-digit publisher codes for ISBNs that start with a 0 from http://blog.openlibrary.org/2009/07/20/isbn-publisher-codes/ where there is also a complete list of publisher codes for ISBNs that start with a 0 or 1.


id: list-of-group-1-isbn-publisher-codes-20260505-0
file: data/en.wikipedia.org/wiki/List_of_group-1_ISBN_publisher_codes-0.md
category: reference
title: List of group-1 ISBN publisher codes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_group-1_ISBN_publisher_codes
date_saved: 2026-05-05T08:19:10.811646+00:00
instance: kb-cron
parent: list-of-group-1-isbn-publisher-codes-20260505-0
summary:
A list of publisher codes for (978) International Standard Book Numbers with a group code of one. (Data from published items by these publishers.) == Assignment == The group-1 publisher codes are assigned as follows: == 2-digit publisher codes == == 3-digit publisher codes == == 4-digit publisher codes == == 5-digit publisher codes == == 6-digit publisher codes == == 7-digit publisher codes == == See also == List of group-0 ISBN publisher codes List of ISBN identifier groups == References == == External links == https://www.isbn-international.org/range_file_generation http://www.books-by-isbn.com/ http://www.books-by-isbn.com/cg-english_speaking_area_1.html List of 2 and 3-digit publisher codes for ISBNs that start with a 0 from http://blog.openlibrary.org/2009/07/20/isbn-publisher-codes/ where there is also a complete list of publisher codes for ISBNs that start with a 0 or 1.


id: list-of-british-bingo-nicknames-20260505-0
file: data/en.wikipedia.org/wiki/List_of_British_bingo_nicknames-0.md
category: reference
title: List of British bingo nicknames
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_British_bingo_nicknames
date_saved: 2026-05-05T08:19:12.021324+00:00
instance: kb-cron
parent: list-of-british-bingo-nicknames-20260505-0
summary:
In the game of bingo in the United Kingdom, callers announcing the numbers have traditionally used some nicknames to refer to particular numbers if they are drawn. The nicknames are sometimes known by the rhyming phrase 'bingo lingo', and there are rhymes for each number from 1 to 90, some of which date back to 1900. Some traditional games went up to 100. In some clubs, the 'bingo caller' will say the number, with the assembled players intoning the rhyme in a call and response manner, in others, the caller will say the rhyme and the players chant the number. One purpose of the nicknames is to allow called numbers to be clearly understood in a noisy environment. In 2003, Butlins holiday camps introduced some more modern calls devised by a professor of popular culture in an attempt to bring fresh interest to bingo. == Calls == == References == === Citations === === Sources ===


id: list-of-mathematical-constants-20260505-0
file: data/en.wikipedia.org/wiki/List_of_mathematical_constants-0.md
category: reference
title: List of mathematical constants
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_mathematical_constants
date_saved: 2026-05-05T08:19:13.299249+00:00
instance: kb-cron
parent: list-of-mathematical-constants-20260505-0
summary:
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set. Explanations of the symbols in the right hand column can be found by clicking on them. == List == == Mathematical constants sorted by their representations as continued fractions == The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one. Decimal representations are rounded or padded to 10 places if the values are known. == Sequences of constants == == See also == Invariant (mathematics) Glossary of mathematical


id: list-of-dates-predicted-for-apocalyptic-events-20260505-0
file: data/en.wikipedia.org/wiki/List_of_dates_predicted_for_apocalyptic_events-0.md
category: reference
title: List of dates predicted for apocalyptic events
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_dates_predicted_for_apocalyptic_events
date_saved: 2026-05-05T08:19:14.717462+00:00
instance: kb-cron
parent: list-of-dates-predicted-for-apocalyptic-events-20260505-0
summary:
Predictions of apocalyptic events that will result in the extinction of humanity, a collapse of civilization, or the destruction of the planet have been made since at least the beginning of the Common Era. Most predictions are related to Abrahamic religions, often standing for or similar to the eschatological events described in their scriptures. Christian predictions typically refer to events like the Rapture, Great Tribulation, Last Judgment, and the Second Coming of Christ. End-time events are normally predicted to occur within the lifetime of the person making the prediction and are usually made using the Bible—in particular the New Testament—as either the primary or exclusive source for the predictions. This often takes the form of mathematical calculations, such as trying to calculate the point in time where it will have been 6,000 years since the supposed creation of the Earth by the Abrahamic God, which according to the Talmud marks the deadline for the Messiah to appear. Predictions of the end from natural events have also been theorised by various scientists and scientific groups. While these predictions are generally accepted as plausible within the scientific community, the events and phenomena are not expected to occur for hundreds of thousands, or


id: table-of-divisors-20260505-0
file: data/en.wikipedia.org/wiki/Table_of_divisors-0.md
category: reference
title: Table of divisors
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Table_of_divisors
date_saved: 2026-05-05T08:19:15.893082+00:00
instance: kb-cron
parent: table-of-divisors-20260505-0
summary:
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which ⁠n/m⁠ is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since ⁠21/7⁠ = 3 (and therefore 7 is also a divisor of 21). If m is a divisor of n, then so is −m. The tables below only list positive divisors. == Key to the tables == d(n) is the number of the positive divisors of n, including 1 and n itself σ(n) is the sum of the positive divisors of n, including 1 and n itself s(n) is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n a deficient number is greater than the sum of its proper divisors; that is, s(n) < n a perfect number equals the sum of its proper divisors; that is, s(n) = n an abundant number is lesser than the sum of its proper divisors; that is, s(n) > n a highly abundant number has a sum of positive divisors that is greater than


id: e-number-20260505-0
file: data/en.wikipedia.org/wiki/E_number-0.md
category: reference
title: E number
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/E_number
date_saved: 2026-05-05T08:19:17.143071+00:00
instance: kb-cron
parent: e-number-20260505-0
summary:
E numbers, short for Europe numbers, are codes for substances used as food additives, including those found naturally in many foods, such as vitamin C, for use within the European Union (EU) and European Free Trade Association (EFTA). Commonly found on food labels, their safety assessment and approval are the responsibility of the European Food Safety Authority (EFSA). The fact that an additive has an E number implies that its use was at one time permitted in products for sale in the European Single Market; some of these additives are no longer allowed today. Having a single unified list for food additives was first agreed upon in 1962 with food colouring. In 1964, the directives for preservatives were added; In 1970 antioxidants were added; In 1974 emulsifiers, stabilisers, thickeners and gelling agents were added as well. == Numbering schemes == The numbering scheme follows that of the International Numbering System (INS) as determined by the Codex Alimentarius committee, though only a subset of the INS additives are approved for use in the European Union as food additives. Outside the European continent plus Russia, E numbers are also encountered on food labelling in other jurisdictions, including the Gulf Cooperation Council, South


id: list-of-integer-sequences-20260505-0
file: data/en.wikipedia.org/wiki/List_of_integer_sequences-0.md
category: reference
title: List of integer sequences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_integer_sequences
date_saved: 2026-05-05T08:19:18.511115+00:00
instance: kb-cron
parent: list-of-integer-sequences-20260505-0
summary:
This is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences. == General == == Figurate numbers == == Types of primes == == Base-dependent == == References == OEIS core sequences == External links == Index to OEIS


id: list-of-isbn-registration-groups-20260505-0
file: data/en.wikipedia.org/wiki/List_of_ISBN_registration_groups-0.md
category: reference
title: List of ISBN registration groups
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_ISBN_registration_groups
date_saved: 2026-05-05T08:19:19.769731+00:00
instance: kb-cron
parent: list-of-isbn-registration-groups-20260505-0
summary:
The registration group or identifier group is the second element in a 13-digit ISBN (first element in a 10-digit ISBN) and indicates the country, geographic region, or language area where a book was published. The element ranges from one to five numerical digits. In 2007, the length of an ISBN changed from 10 to 13 digits, and a new 3-digit prefix (978 or 979) was added in front of 10-digit ISBNs. The following registration groups are compatible with or without a 978- prefix: 0–5 600–639 65–66 69990–69999 7 80–94 950–989 9900–9989 99900–99999 The following must have a 979- prefix: (979-0 is reserved for International Standard Music Numbers for sheet music) 979-10 through 979-13 979-8 Shorter registration group numbers are generally used for countries or regions with greater publishing volume. Because a longer number leaves room for fewer publishers and ISBNs, several countries have more than one number assigned. On the other hand, some countries (Australia, Switzerland, Fiji) have no unique number because they fall in a broader geographic region or language area. == With 10-digit ISBN or 978- prefix == === Prefixes of length 1 === === Prefixes of length 2 === === Prefixes of length 3 === === Prefixes


id: significance-of-numbers-in-judaism-20260505-0
file: data/en.wikipedia.org/wiki/Significance_of_numbers_in_Judaism-0.md
category: reference
title: Significance of numbers in Judaism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Significance_of_numbers_in_Judaism
date_saved: 2026-05-05T08:19:21.096993+00:00
instance: kb-cron
parent: significance-of-numbers-in-judaism-20260505-0
summary:
Various numbers play a significant role in Jewish texts or practice. Some such numbers were used as mnemonics to help remember concepts, while other numbers were considered to have intrinsic significance or allusive meaning. The song Echad Mi Yodea ("who knows one?"), sung at the Passover Seder, is known for recounting a religious concept or practice associated with each of the first 13 numbers. == In Jewish History == In Jewish historical study, numbers were believed to be a means for understanding the divine. This marriage between the symbolic and the physical found its pinnacle in the creation of the Tabernacle. The numerical dimensions of the temple are a "microcosm of creation ... that God used to create the Olamot-Universes." In the thought system of Maharal, each number has a consistent philosophical meaning: unity. dualism and multiplicity. the unity between two extremes. multiplicity in two directions, like the cardinal directions. the center point which unifies those four extremes. multiplicity in three dimensions. the center point which unifies all of nature, as with Shabbat. the supernatural realm which feeds nature, and the striving of man for a connection with the supernatural. the most complete multiplicity, including division between the natural and


id: significance-of-numbers-in-judaism-20260505-1
file: data/en.wikipedia.org/wiki/Significance_of_numbers_in_Judaism-1.md
category: reference
title: Significance of numbers in Judaism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Significance_of_numbers_in_Judaism
date_saved: 2026-05-05T08:19:21.096993+00:00
instance: kb-cron
parent: significance-of-numbers-in-judaism-20260505-0
summary:
== 8 == Eight are the days of the circumcision - שמונה ימי מילה Total number of days of Yom Tov in a year in Israel Number of days of Chanukah 8 days of sukkos Number of days of Pesach (Diaspora) According to the Zohar, the number eight signifies new beginnings because the eighth day was the first day after creation when God returned to work; the week began again. == 9 == The first nine days of the Hebrew month of Av are collectively known as "The Nine Days" (Tisha HaYamim), and are a period of semi-mourning leading up to Tisha B'Av, the ninth day of Av on which both Temples in Jerusalem were destroyed == 10 == The Ten Commandments - עשרה דיבריא The ten Plagues of Egypt Ten Jewish people form a minyan There are ten Sefirot (human and Godly characteristics) depicted in Kabbalah According to the Mishna, the world was created by ten divine utterances; ten generations passed between Adam and Noah and between Noah and Abraham; Abraham received ten trials from God; the Israelites received ten trials in the desert; there were ten plagues in Egypt; ten miracles occurred in the Temple; ten apparently supernatural


id: significance-of-numbers-in-judaism-20260505-2
file: data/en.wikipedia.org/wiki/Significance_of_numbers_in_Judaism-2.md
category: reference
title: Significance of numbers in Judaism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Significance_of_numbers_in_Judaism
date_saved: 2026-05-05T08:19:21.096993+00:00
instance: kb-cron
parent: significance-of-numbers-in-judaism-20260505-0
summary:
== 40 == Moses stayed on mount Sinai for 40 days after the giving of Torah. After the golden calf, he spend there another 40 days (and nights) The number of days the spies were in the land of Canaan Years in the desert—a generation Just as Mozes, the reign of king David and Solomon was also 40 years Days and nights of rain during the flood that occurred at the time of Noah Isaac's age at marriage to Rebecca Esau's age at marriage to his first two wives Number of days Jonah prophesies will pass before Nineveh is destroyed. (They repent) A mikveh must contain at least 40 se'ah (volume measurement) of water Number of years of the reign of David, Solomon, and the most righteous judges in the book of Judges Number of lashes for one who transgresses a commandment Number of days which the Torah was given Number of weeks a person is formed in their mother's womb Number of curses on Adam Minimum age at which a man could join the Sanhedrin == 42 == Letters in one of God's Divine Names 42 cities that refugees (See Cities of Refuge) can go to when they kill


id: list-of-prime-numbers-20260505-0
file: data/en.wikipedia.org/wiki/List_of_prime_numbers-0.md
category: reference
title: List of prime numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_prime_numbers
date_saved: 2026-05-05T08:19:22.349003+00:00
instance: kb-cron
parent: list-of-prime-numbers-20260505-0
summary:
This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes. The first 1,000 primes are listed below, followed by lists of notable types of prime numbers in alphabetical order, giving their respective first terms. The number 1 is neither prime nor composite. == The first 1,000 prime numbers == The following table lists the first 1,000 primes, with 20 columns of consecutive primes in each of the 50 rows. (sequence A000040 in the OEIS). The Goldbach conjecture verification project reports that it has computed all primes smaller than 4×1018. That means 95,676,260,903,887,607 primes (nearly 1017), but they were not stored. There are known formulae to evaluate the prime-counting function (the number of primes smaller than a given value) faster than computing the primes. This has been used to compute that there are 1,925,320,391,606,803,968,923 primes (roughly 2×1021) smaller than 1023. A different computation found that there are 18,435,599,767,349,200,867,866 primes (roughly 2×1022) smaller than 1024, if the Riemann


id: list-of-prime-numbers-20260505-1
file: data/en.wikipedia.org/wiki/List_of_prime_numbers-1.md
category: reference
title: List of prime numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_prime_numbers
date_saved: 2026-05-05T08:19:22.349003+00:00
instance: kb-cron
parent: list-of-prime-numbers-20260505-0
summary:
Real Eisenstein primes are real Eisenstein integers that are irreducible. Equivalently, they are primes of the form 3k − 1, for a positive integer k. 2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401 (OEIS: A003627) === Emirps === Emirps are primes that become a different prime after their base 10 digits have been reversed. The name "emirp" is the reverse of the word "prime". 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991 (OEIS: A006567) === Euclid primes === Euclid primes are primes p such that p−1 is a primorial. 3, 7, 31, 211, 2311, 200560490131 (OEIS: A018239) === Euler irregular primes === Euler irregular primes are primes p {\displaystyle p} that divide an Euler number E 2 n , {\displaystyle E_{2n},} for some 0 ≤ 2 n ≤ p − 3. {\displaystyle 0\leq 2n\leq p-3.} 19, 31, 43, 47,


id: list-of-prime-numbers-20260505-2
file: data/en.wikipedia.org/wiki/List_of_prime_numbers-2.md
category: reference
title: List of prime numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_prime_numbers
date_saved: 2026-05-05T08:19:22.349003+00:00
instance: kb-cron
parent: list-of-prime-numbers-20260505-0
summary:
The (p, p - 3) irregular primes are primes p such that (p, p − 3) is an irregular pair. 16843, 2124679 (OEIS: A088164) ==== (p, p − 5) irregular primes ==== The (p, p - 5) irregular primes are primes p such that (p, p − 5) is an irregular pair. 37 ==== (p, p − 9) irregular primes ==== The (p, p - 9) irregular primes are primes p such that (p, p − 9) is an irregular pair. 67, 877 (OEIS: A212557) === Isolated primes === Isolated primes are primes p such that both p − 2 and p + 2 are both composite. 2, 23, 37, 47, 53, 67, 79, 83, 89, 97, 113, 127, 131, 157, 163, 167, 173, 211, 223, 233, 251, 257, 263, 277, 293, 307, 317, 331, 337, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 439, 443, 449, 457, 467, 479, 487, 491, 499, 503, 509, 541, 547, 557, 563, 577, 587, 593, 607, 613, 631, 647, 653, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 839, 853, 863, 877, 887, 907, 911, 919, 929, 937, 941, 947, 953,


id: list-of-prime-numbers-20260505-3
file: data/en.wikipedia.org/wiki/List_of_prime_numbers-3.md
category: reference
title: List of prime numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_prime_numbers
date_saved: 2026-05-05T08:19:22.349003+00:00
instance: kb-cron
parent: list-of-prime-numbers-20260505-0
summary:
Primes that remain the same when their decimal digits are read backwards. 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741 (OEIS: A002385) === Palindromic wing primes === Primes of the form a ( 10 m − 1 ) 9 ± b × 10 m − 1 2 {\displaystyle {\frac {a{\big (}10^{m}-1{\big )}}{9}}\pm b\times 10^{\frac {m-1}{2}}} with 0 ≤ a ± b < 10 {\displaystyle 0\leq a\pm b<10} . This means all digits except the middle digit are equal. 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 11311, 11411, 33533, 77377, 77477, 77977, 1114111, 1117111, 3331333, 3337333, 7772777, 7774777, 7778777, 111181111, 111191111, 777767777, 77777677777, 99999199999 (OEIS: A077798) === Partition primes === Partition function values that are prime. 2, 3, 5, 7, 11, 101, 17977, 10619863, 6620830889, 80630964769, 228204732751, 1171432692373, 1398341745571, 10963707205259, 15285151248481, 10657331232548839, 790738119649411319, 18987964267331664557 (OEIS: A049575) === Pell primes === Primes in the Pell number sequence P0 = 0, P1 = 1, Pn = 2Pn−1 + Pn−2. 2, 5, 29, 5741, 33461, 44560482149, 1746860020068409, 68480406462161287469, 13558774610046711780701, 4125636888562548868221559797461449 (OEIS:


id: list-of-prime-numbers-20260505-4
file: data/en.wikipedia.org/wiki/List_of_prime_numbers-4.md
category: reference
title: List of prime numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_prime_numbers
date_saved: 2026-05-05T08:19:22.349003+00:00
instance: kb-cron
parent: list-of-prime-numbers-20260505-0
summary:
Of the form an + d for fixed integers a and d. Also called primes congruent to d modulo a. The primes of the form 2n+1 are the odd primes, including all primes other than 2. Some sequences have alternate names: 4n+1 are the Pythagorean primes, 4n+3 are the integer Gaussian primes, and 6n+5 are the Eisenstein primes (with 2 omitted). The classes 10n+d (d = 1, 3, 7, 9) are primes ending in the decimal digit d. If a and d are relatively prime, the arithmetic progression contains infinitely many primes. 2n+1: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 (OEIS: A065091) 4n+1: 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137 (OEIS: A002144) 4n+3: 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107 (OEIS: A002145) 6n+1: 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139 (OEIS: A002476) 6n+5: 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113 (OEIS: A007528) 8n+1: 17, 41, 73, 89, 97, 113, 137, 193, 233, 241, 257, 281, 313, 337, 353 (OEIS: A007519)


id: list-of-prime-numbers-20260505-5
file: data/en.wikipedia.org/wiki/List_of_prime_numbers-5.md
category: reference
title: List of prime numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_prime_numbers
date_saved: 2026-05-05T08:19:22.349003+00:00
instance: kb-cron
parent: list-of-prime-numbers-20260505-0
summary:
==== Left-truncatable ==== Primes that remain prime when the leading decimal digit is successively removed. 2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197, 223, 283, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 523, 547, 613, 617, 643, 647, 653, 673, 683 (OEIS: A024785) ==== Right-truncatable ==== Primes that remain prime when the least significant decimal digit is successively removed. 2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797 (OEIS: A024770) ==== Two-sided ==== Primes that are both left-truncatable and right-truncatable. There are exactly fifteen two-sided primes: 2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397 (OEIS: A020994) === Twin primes === Where (p, p+2) are both prime. (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193), (197, 199), (227, 229), (239, 241), (269, 271), (281, 283), (311, 313), (347, 349),


id: table-of-prime-factors-20260505-0
file: data/en.wikipedia.org/wiki/Table_of_prime_factors-0.md
category: reference
title: Table of prime factors
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Table_of_prime_factors
date_saved: 2026-05-05T08:19:23.562059+00:00
instance: kb-cron
parent: table-of-prime-factors-20260505-0
summary:
The tables contain the prime factorization of the natural numbers from 1 to 1000. When n is a prime number, the prime factorization is just n itself, written in bold below. The number 1 is called a unit. It has no prime factors and is neither prime nor composite. == Properties == Many properties of a natural number n {\displaystyle n} can be seen or directly computed from the prime factorization of n {\displaystyle n} . The multiplicity of a prime factor p {\displaystyle p} of n {\displaystyle n} is the largest exponent m {\displaystyle m} for which p m {\displaystyle p^{m}} divides n {\displaystyle n} . The tables show the multiplicity for each prime factor. If no exponent is written then the multiplicity is 1 {\displaystyle 1} (since p = p 1 {\displaystyle p=p^{1}} ). The multiplicity of a prime which does not divide n {\displaystyle n} may be called 0 {\displaystyle 0} or may be considered undefined. ω ( n ) {\displaystyle \omega (n)} and Ω ( n ) {\displaystyle \Omega (n)} , the prime omega functions, count the number of prime factors of a natural number n {\displaystyle n} . ω ( n ) {\displaystyle \omega (n)}


id: table-of-prime-factors-20260505-1
file: data/en.wikipedia.org/wiki/Table_of_prime_factors-1.md
category: reference
title: Table of prime factors
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Table_of_prime_factors
date_saved: 2026-05-05T08:19:23.562059+00:00
instance: kb-cron
parent: table-of-prime-factors-20260505-0
summary:
a 0 ( n ) {\displaystyle a_{0}(n)} , sometimes called the integer logarithm, is the sum of primes dividing n {\displaystyle n} , counted with multiplicity. It is an additive function. A Ruth-Aaron pair is a pair of two consecutive numbers ( n , n + 1 ) {\displaystyle (n,n+1)} with a 0 ( n ) = a 0 ( n + 1 ) {\displaystyle a_{0}(n)=a_{0}(n+1)} . The first (by n {\displaystyle n} value): 5, 8, 15, 77, 125, 714, 948, 1330, 1520, 1862, 2491, 3248 (sequence A039752 in the OEIS). Another definition is where the same prime is only counted once; if so, the first (by n {\displaystyle n} value): 5, 24, 49, 77, 104, 153, 369, 492, 714, 1682, 2107, 2299 (sequence A006145 in the OEIS). A primorial p n # {\displaystyle p_{n}\#} is the product of all primes from 2 to p n {\displaystyle p_{n}} . The first: 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810 (sequence A002110 in the OEIS). 1 # = 1 {\displaystyle 1\#=1} is sometimes included. A factorial n ! {\displaystyle n!} is the product of all numbers from 1 to n {\displaystyle n} . The first: 1, 2,


id: recycling-codes-20260505-0
file: data/en.wikipedia.org/wiki/Recycling_codes-0.md
category: reference
title: Recycling codes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Recycling_codes
date_saved: 2026-05-05T08:19:24.672496+00:00
instance: kb-cron
parent: recycling-codes-20260505-0
summary:
Recycling codes are used to identify the materials out of which the item is made, to facilitate easier recycling process. The presence on an item of a recycling code, a chasing arrows logo, or a resin code, is not an automatic indicator that a material is recyclable; it is an explanation of what the item is made of. Codes have been developed for batteries, biomatter/organic material, glass, metals, paper, and plastics. Various countries have adopted different codes. For example, the table below shows the polymer resin (plastic) codes. In the United States there are fewer, because ABS is placed with "others" in group 7. A number of countries have a finer-grained system with more recycling codes. For example, China's polymer identification system has seven different classifications of plastic, five different symbols for post-consumer paths, and 140 identification codes. The lack of a code system in some countries has encouraged those who fabricate their own plastic products, such as RepRap and other prosumer 3-D printer users, to adopt a voluntary recycling code based on the more comprehensive Chinese system. == Resin identification codes and codes defined by the European Commission == == Chinese codes for plastics products == The Standardization Administration


id: list-of-numeral-systems-20260505-0
file: data/en.wikipedia.org/wiki/List_of_numeral_systems-0.md
category: reference
title: List of numeral systems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_numeral_systems
date_saved: 2026-05-05T08:19:25.906324+00:00
instance: kb-cron
parent: list-of-numeral-systems-20260505-0
summary:
There are many different numeral systems, that is, writing systems for expressing numbers. == By culture / time period == "A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. Some systems have two bases, a smaller (subbase) and a larger (base); an example is Roman numerals, which are organized by fives (V=5, L=50, D=500, the subbase) and tens (X=10, C=100, M=1,000, the base). == By type of notation == Numeral systems are classified here as to whether they use positional notation (also known as place-value notation), and further categorized by radix or base. === Standard positional numeral systems === The common names are derived somewhat arbitrarily from a mix of Latin and Greek, in some cases including roots from both languages within a single name. There have been some proposals for standardisation. === Non-standard positional numeral systems === ==== Bijective numeration ==== ==== Signed-digit representation ==== ==== Complex bases ==== ==== Non-integer bases ==== ==== n-adic number


id: list-of-types-of-numbers-20260505-0
file: data/en.wikipedia.org/wiki/List_of_types_of_numbers-0.md
category: reference
title: List of types of numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_types_of_numbers
date_saved: 2026-05-05T08:19:27.311797+00:00
instance: kb-cron
parent: list-of-types-of-numbers-20260505-0
summary:
Numbers can be classified according to how they are represented or according to the properties that they have. == Main types == Natural numbers ( N {\displaystyle \mathbb {N} } ): The counting numbers {1, 2, 3, ...} are commonly called natural numbers; however, other definitions include 0, so that the non-negative integers {0, 1, 2, 3, ...} are also called natural numbers. Natural numbers including 0 are also sometimes called whole numbers. Alternatively natural numbers not including 0 are also sometimes called whole numbers instead. Integers ( Z {\displaystyle \mathbb {Z} } ): Positive and negative counting numbers, as well as zero: {..., −3, −2, −1, 0, 1, 2, 3, ...}. Rational numbers ( Q {\displaystyle \mathbb {Q} } ): Numbers that can be expressed as a ratio of an integer to a non-zero integer. All integers are rational, but there are rational numbers that are not integers, such as −2/9. Real numbers ( R {\displaystyle \mathbb {R} } ): Numbers that correspond to points along a line. They can be positive, negative, or zero. All rational numbers are real, but the converse is not true. Irrational numbers ( R ∖ Q {\displaystyle \mathbb {R} \setminus \mathbb {Q} }


id: list-of-types-of-numbers-20260505-1
file: data/en.wikipedia.org/wiki/List_of_types_of_numbers-1.md
category: reference
title: List of types of numbers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_types_of_numbers
date_saved: 2026-05-05T08:19:27.311797+00:00
instance: kb-cron
parent: list-of-types-of-numbers-20260505-0
summary:
== Algebraic numbers == Algebraic number: Any number that is the root of a non-zero polynomial with rational coefficients. Transcendental number: Any real or complex number that is not algebraic. Examples include e and π. Trigonometric number: Any number that is the sine or cosine of a rational multiple of π. Quadratic surd: A root of a quadratic equation with rational coefficients. Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds. Algebraic integer: A root of a monic polynomial with integer coefficients. == Non-standard numbers == Transfinite numbers: Numbers that are greater than any natural number. Ordinal numbers: Finite and infinite numbers used to describe the order type of well-ordered sets. Cardinal numbers: Finite and infinite numbers used to describe the cardinalities of sets. Infinitesimals: These are smaller than any positive real number, but are nonetheless greater than zero. These were used in the initial development of calculus, and are used in synthetic


id: list-of-airborne-wind-energy-organizations-20260505-0
file: data/en.wikipedia.org/wiki/List_of_airborne_wind_energy_organizations-0.md
category: reference
title: List of airborne wind energy organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_airborne_wind_energy_organizations
date_saved: 2026-05-05T08:19:29.973741+00:00
instance: kb-cron
parent: list-of-airborne-wind-energy-organizations-20260505-0
summary:
This is a list of airborne wind energy or kite-energy organizations that are advancing airborne wind energy systems (AWES). In 2011 there were over 40 organizations involved worldwide, but this number has increased to over 60 in 2017. Categories of kite-energy or airborne-wind-energy organizations that are forming the nascent industry: education, academic, non-profit, for-profit, communication, research, original kite-energy equipment manufacturer, kite-line manufacturer, industry-wide association, history, testing, forum entity, library, cooperative, consortium, group, club, school, training school. Generation by kite-energy systems may involve pumping, electricity generators flown in the upper flying system (flygen), electric generators situated on the land or sea or on board a vessel (groundgen), simple lifting of objects (lifting), pulling hulls or other objects (traction), or transportation; systems generate energy to do special tasks. Systems may be scaled from tiny to utility size. == Organizations == == References ==


id: list-of-arctic-research-programs-20260505-0
file: data/en.wikipedia.org/wiki/List_of_Arctic_research_programs-0.md
category: reference
title: List of Arctic research programs
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_Arctic_research_programs
date_saved: 2026-05-05T08:19:31.370560+00:00
instance: kb-cron
parent: list-of-arctic-research-programs-20260505-0
summary:
This is a list of Arctic research programs: Arctic and Antarctic Research Institute Arctic and Northern Studies at University of Alaska Fairbanks Arctic Centre, University of Lapland The Arctic Institute | Center for Circumpolar Security Studies Arctic Institute of North America Arctic Research Consortium of the United States Arctic Research Foundation Arctic Research Office Arctic Submarine Laboratory Arctic Technology Centre Association of Polar Early Career Scientists (APECS) Byrd Polar Research Center Canadian High Arctic Ionospheric Network Centre for Polar Observation & Modelling Circumarctic Environmental Observatories Network Cooperative Institute for Arctic Research EISCAT Flashline Mars Arctic Research Station Institute of Arctic and Alpine Research Institute of Arctic Biology International Arctic Buoy Program International Arctic Research Center International Arctic Science Committee Malaurie Institute of Arctic Research Monaco-UVSQ National Centre for Polar and Ocean Research North Greenland Ice Core Project National Snow and Ice Data Center QUEEN SCICEX Scott Polar Research Institute Surface Heat Budget of the Arctic Ocean United States Arctic Research Commission University of the Arctic == See also == List of research stations in the Arctic


id: atmospheric-chemistry-observational-databases-20260505-0
file: data/en.wikipedia.org/wiki/Atmospheric_chemistry_observational_databases-0.md
category: reference
title: Atmospheric chemistry observational databases
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Atmospheric_chemistry_observational_databases
date_saved: 2026-05-05T08:19:32.580210+00:00
instance: kb-cron
parent: atmospheric-chemistry-observational-databases-20260505-0
summary:
Over the last two centuries many environmental chemical observations have been made from a variety of ground-based, airborne, and orbital platforms and deposited in databases. Many of these databases are publicly available. All of the instruments mentioned in this article give online public access to their data. These observations are critical in developing our understanding of the Earth's atmosphere and issues such as climate change, ozone depletion and air quality. Some of the external links provide repositories of many of these datasets in one place. For example, the Cambridge Atmospheric Chemical Database, is a large database in a uniform ASCII format. Each observation is augmented with the meteorological conditions such as the temperature, potential temperature, geopotential height, and equivalent PV latitude. == Ground-based and balloon observations == NDSC observations. The Network for the Detection for Stratospheric Change (NDSC) is a set of high-quality remote-sounding research stations for observing and understanding the physical and chemical state of the stratosphere. Ozone and key ozone-related chemical compounds and parameters are targeted for measurement. The NDSC is a major component of the international upper atmosphere research effort and has been endorsed by national and international scientific agencies, including the International Ozone Commission, the United


id: atmospheric-chemistry-observational-databases-20260505-1
file: data/en.wikipedia.org/wiki/Atmospheric_chemistry_observational_databases-1.md
category: reference
title: Atmospheric chemistry observational databases
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Atmospheric_chemistry_observational_databases
date_saved: 2026-05-05T08:19:32.580210+00:00
instance: kb-cron
parent: atmospheric-chemistry-observational-databases-20260505-0
summary:
== Space shuttle observations == ATMOS observations. The Atmospheric Trace Molecule Spectroscopy experiment (ATMOS) is an infrared spectrometer (a Fourier transform interferometer) that is designed to study the chemical composition of the atmosphere. In this section you will be able to read both general and detailed information as to why and how the instrument works. The ATMOS instrument has flown four times on the Space Shuttle since 1985. The predecessor to ATMOS, flown on aircraft and high-altitude balloon platforms, was born in the early 1970s out of concern for the effects of Super Sonic Transport exhaust products on the ozone layer. The experiment was redesigned for the Space Shuttle when the potential for ozone destruction by man-made chlorofluorocarbons was discovered and the need for global measurements became crucial. CRISTA observations. CRISTA is short for CRyogenic Infrared Spectrometers and Telescopes for the Atmosphere. It is a limb-scanning satellite experiment, designed and developed by the University of Wuppertal to measure infrared emissions of the Earth's atmosphere. Equipped with three telescopes and four spectrometers and cooled with liquid helium, CRISTA acquires global maps of temperature and atmospheric trace gases with very high horizontal and vertical resolution. The design enables the observation of small


id: list-of-bioinformatics-institutions-20260505-0
file: data/en.wikipedia.org/wiki/List_of_bioinformatics_institutions-0.md
category: reference
title: List of bioinformatics institutions
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_bioinformatics_institutions
date_saved: 2026-05-05T08:19:33.801986+00:00
instance: kb-cron
parent: list-of-bioinformatics-institutions-20260505-0
summary:
This is a list of major bioinformatics institutions. National Center for Biotechnology Information (NCBI) European Bioinformatics Institute (EMBL-EBI) Australia Bioinformatics Resource (EMBL-ABR) Swiss Institute of Bioinformatics (SIB) Scripps Research Institute (TSRI) European Molecular Biology Laboratory (EMBL) Wellcome Trust Sanger Institute (WTSI) Computational Biology Department Broad Institute Whitehead Institute The Institute for Genomic Research Center for Biomolecular Science and Engineering Netherlands Bioinformatics Centre COSBI Institute of Bioinformatics (IOB) Max Planck Institute for Molecular Cell Biology and Genetics (MPI-CBG) Partner Institute for Computational Biology Flatiron Institute DDBJ Center (DDBJ) Bioinformatics Institute (Singapore) Database Center for Life Science (DBCLS) == References == Benue state university department of Anatomy


id: canadian-university-scientific-research-organizations-20260505-0
file: data/en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations-0.md
category: reference
title: Canadian university scientific research organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations
date_saved: 2026-05-05T08:19:35.071794+00:00
instance: kb-cron
parent: canadian-university-scientific-research-organizations-20260505-0
summary:
Expenditures by Canadian universities on scientific research and development accounted for about 40% of all spending on scientific research and development in Canada in 2006. Research in the natural and social sciences in Canada, with a few important exceptions, is almost exclusively funded by the Canadian taxpayer and is distributed to universities by five important federal funding agencies, the Natural Sciences and Engineering Research Council (NSERC), the Canadian Institutes of Health Research (CIHR), and the Social Sciences and Humanities Research Council of Canada (SSHRC). Additional monies are also provided by the Canada Research Chairs organization, which provides financing for the staffing of research personnel at Canadian universities and the Canada Foundation for Innovation, which supports the acquisition of scientific research infrastructure by Canadian universities, colleges, research hospitals, and non-profit research institutions. In 2006, total spending on scientific and industrial research in Canada amounted to C$28.067 billion or about 2 percent of GDP. In 2006, Canadian universities spent C$10.890 billion on research and development, representing about 40 percent of all R&D spending in Canada and about .66 percent of Canada's GDP. Below are the names of those university institutions that carry out both natural and social science research, although the emphasis


id: canadian-university-scientific-research-organizations-20260505-1
file: data/en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations-1.md
category: reference
title: Canadian university scientific research organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations
date_saved: 2026-05-05T08:19:35.071794+00:00
instance: kb-cron
parent: canadian-university-scientific-research-organizations-20260505-0
summary:
Alberta Poultry Research Centre Alberta Veterinary Research Institute (AVRI) Canada Science & Research Institute Inc (CSRI/Non Gov/Tr Labs Partner) Centre for Enhanced Forest Management (EFM) Dairy Research and Technology Centre (DRTC) Environmental Research and Studies Centre Material Culture Institute (MCI) Engineering Alberta Centre for Surface Engineering and Science Construction Research Institute for Canada (CIRC) Imperial Oil Centre for Oil Sands Innovation Health Sciences Council Alberta Centre on Aging Alberta Institute for Human Nutrition Community-University Partnership (CUP) The John Dossetor Health Ethics Centre Medicine and Dentistry Alberta Asthma Centre Alberta Centre for Prions and Protein Folding Diseases Alberta Diabetes Research Institute Alberta Institute for Viral Immunology (AIVI) Alberta Peptide Institute (API) Alberta Transplant Applied Genomics Centre (ATAGC) Canadian VIGOUR Centre Centre for Health Evidence Centre for Neuroscience Digestive Health Care Centre for Colon Cancer (DHCCC) Glaxo Wellcome Heritage Research Institute Magnetic Resonance Diagnostics Centre (MRDC) Muttart Diabetes Research & Training Centre Perinatal Research Group Women and Children's Health Research Institute (WCHRI) Nursing Institute for Philosophical Nursing Research International Institute for Qualitative Methodology International Nursing Centre Pharmacy and Pharmaceutical Sciences Centre for Community Pharmacy Research and Interdisciplinary Studies (c/COMPRIS) Noujaim Institute School of Public Health Alberta Centre for Injury Control and Research


id: canadian-university-scientific-research-organizations-20260505-2
file: data/en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations-2.md
category: reference
title: Canadian university scientific research organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations
date_saved: 2026-05-05T08:19:35.071794+00:00
instance: kb-cron
parent: canadian-university-scientific-research-organizations-20260505-0
summary:
==== Research centres and institutes ==== Canadian Centre of Arts & Technology (CCAT) Canadian Centre for Cultural Innovation (CCCI) Centre for Accounting Research & Education (CARE) Centre for Advanced Studies in Finance (CASF) Centre for Advancement of Trenchless Technologies at Waterloo (CATT) Centre for Applied Cryptographic Research (CACR) Centre for Business, Entrepreneurship & Technology (CBET) Centre for Computational Mathematics in Industry & Commerce (CCMIC) Centre for Contact Lens Research (CCLR) Centre for Cultural Management (CCM) Centre for Education in Mathematics & Computing (CEMC) Centre for Mental Health Research (CMHR) Centre for Molecular Beams & Laser Chemistry Centre for Theoretical Neuroscience Heritage Resource Centre Institute for Computer Research (ICR) Institute for Innovation Research (IIR) Institute for Polymer Research (IPR) Institute for Quantitative Finance & Insurance (IQFI) Institute for Quantum Computing (IQC) Institute for Risk Research (IRR) Institute for Vision Science & Technology (IVST) Institute of Biochemistry & Molecular Biology Institute of Insurance and Pension Research (IIPR) Integrated Centre for Visualization, Design & Manufacturing (ICVDM) Mid-Size City Research Centre (MCRC) Nortel Networks Institute for Advanced Information Technology (NNI) Schlegel – UW Research Institute for Aging (RIA) Survey Research Centre (SRC) Waterloo Centre for the Advancement of Co-operative Education (WatCACE) Waterloo Centre for


id: canadian-university-scientific-research-organizations-20260505-3
file: data/en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations-3.md
category: reference
title: Canadian university scientific research organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations
date_saved: 2026-05-05T08:19:35.071794+00:00
instance: kb-cron
parent: canadian-university-scientific-research-organizations-20260505-0
summary:
==== Centres de recherche ==== Agora Jules Dupuit (AJD) Centre d'excellence en Centre Canadien d'études allemandes et européennes (CCEAE) Centre d'excellence en Centre d'études et de recherches internationales (CERIUM) Centre d'excellence en Centre d'études ethniques des universités montréalaises (CEETUM) Centre d'excellence en Centre d'étude des religions de l'Université de Montréal (CERUM) Centre d'excellence en neuromique (CEN) Centre d'excellence en Centre d'excellence pour le développement des jeunes enfants (CEDJE) Centre d'excellence en Centre de droit des affaires et du commerce international (CDACI) Centre d'excellence en Centre de formation et d'expertise en recherche en administration des services infirmiers (FERASI) Centre d'excellence en Centre de recherche en droit public (CRDP) Centre d'excellence en Centre de recherche en éthique de l'Université de Montréal (CREUM) Centre d'excellence en Centre de recherche en neuropsychologie et cognition (CERNEC) Centre de recherche en reproduction animale (CRRA) Centre de recherche en sciences neurologiques (CRSN) Centre de recherche interdisciplinaire sur la violence familiale et la violence faite aux ** femmes (CRI-VIFF) Centre de recherche interdisciplinaire sur les problèmes conjugaux et les aggressions ** sexuelles (CRIPCAS) Centre de recherche interdisciplinaire sur les technologies émergentes (CITÉ) Centre de recherche interuniversitaire sur la formation et la profession enseignante (CRIFPE) Centre de recherche interuniversitaire


id: canadian-university-scientific-research-organizations-20260505-4
file: data/en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations-4.md
category: reference
title: Canadian university scientific research organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations
date_saved: 2026-05-05T08:19:35.071794+00:00
instance: kb-cron
parent: canadian-university-scientific-research-organizations-20260505-0
summary:
=== Queen's University === Kingston, Ontario NSERC Funding 2003: C$M 21,571 Number of Canada Research Chairs – 54 ==== University centres and institutes ==== Centre for Neuroscience Studies (formerly Centre for the Study of Molecular Neuroscience) Centre for Water and the Environment GeoEngineering Centre High Performance Computing Virtual Laboratory (HPCVL) Human Mobility Research Centre Sudbury Neutrino Observatory Institute Southern African Research Centre ==== Faculty centres and institutes ==== Cancer Research Institute Cancer Clinical Trials Division Cancer Biology & Genetics Division Cancer Care & Epidemiology Division Centre for Health Services and Policy Research Centre for International Relations Charles Pentland Centre for Manufacturing of Advanced Ceramics and Nanomaterials Vladimir Krstic Centre for Studies in Primary Care Richard Birtwhistle Centre for the Study of Democracy Fuel Cell Research Centre John Deutsch Institute for the Study of Economic Policy Industrial Relations Centre Institute for Intergovernmental Relations Thomas Courchene The Monieson Centre Yolande Chan Surveillance Studies Centre, David Murakami Wood === McMaster University === Hamilton, Ontario. NSERC Funding 2003: C$M 20,694 Number of Canada Research Chairs – 62 ==== Research institutes ==== Origins Institute McMaster Institute for Applied Radiation Sciences(McIARS) McMaster Institute for Energy Studies McMaster Institute of Environment & Health Institute on Globalization and


id: canadian-university-scientific-research-organizations-20260505-5
file: data/en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations-5.md
category: reference
title: Canadian university scientific research organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations
date_saved: 2026-05-05T08:19:35.071794+00:00
instance: kb-cron
parent: canadian-university-scientific-research-organizations-20260505-0
summary:
==== University research institutes and centres ==== Alberta Global Forum Calgary Centre for Financial Research – under development Calgary Centre for Innovative Technology (CCIT) Calgary Institute for the Humanities] Canadian Centre for the Study of Higher Education Centre for Advanced Technologies of Life Sciences (CAT) Centre for Bioengineering Research and Education (CBRE) Centre for Environmental Engineering Research and Education (CEERE) Centre for Gifted Education Centre for Health and Policy Studies (CHAPS) Centre for Information Security and Cryptography Centre for Innovation Studies (THECIS) Centre for Mathematics in Life Sciences Centre for Microsystems Engineering (CME) Centre for Military and Strategic Studies (CMSS) Centre for Public Interest Accounting (CPIA) Centre for Research in the Fine Arts (CRFA) Centre for Social Work Research and Development iNFORMATICS Research Centre Institute for Advanced Policy Research Institute for Biocomplexity and Informatics Institute for Gender Research Institute for Quantum Science and Technology (formerly the Institute for Quantum Information Science) Institute for Space Research Institute for Sustainable Energy, Environment and Economy Institute for United States Policy Research Institute of Professional Communication (IPC) International Institute for Resource Industries and Sustainable Studies (IRIS) Kananaskis Field Stations Language Research Centre Latin American Research Centre (LARC) Markin Institute for Public Health Pipeline Engineering


id: canadian-university-scientific-research-organizations-20260505-6
file: data/en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations-6.md
category: reference
title: Canadian university scientific research organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations
date_saved: 2026-05-05T08:19:35.071794+00:00
instance: kb-cron
parent: canadian-university-scientific-research-organizations-20260505-0
summary:
==== Research centres, institutes, and groups ==== Atlantic Centre of Excellence for Women's Health Atlantic Health Promotion Research Centre Atlantic Institute of Criminology Atlantic Research Data Centre (ARDC) Centre for African Studies Centre for Foreign Policy Studies Dalhousie Infectious Disease Research Alliance (DIDRA) Dalhousie Inflammation Group Dalhousie Multiple Sclerosis Research Unit Energy at Dalhousie Health Law Institute International Ocean Institute Law and Technology Institute Marine and Environmental Law Institute Neuroscience Institute Pediatric Pain Research Lab Population Health Research Unit (PHRU) Institute for Research in Materials ==== Technical research facilities ==== Aquatron Atlantic Region Magnetic Resonance Centre Canadian Institute of Fisheries Technology (CIFT) Canadian Residential Energy End-use Data and Analysis Center (CREEDAC) Centre for Water Resources Studies (CWRS) Cosmogenic Nuclide Exposure Dating Facility Minerals Engineering Centre (MEC) Nova Scotia CAD/CAM Centre (NSCCC) Slowpoke Facility Trace Analysis Research Centre (TARC) ==== Affiliated research organizations ==== IWK Health Centre Global Information Networking Institute The Nova Scotia Hospital, QEII Health Sciences Centre Saint John Regional Hospital === University of Ottawa === Ottawa, Ontario. NSERC Funding 2003: C$M 14,127 Number of Canada Research Chairs – 49 ==== uOttawa research centres and institutes ==== Centre for Advanced Research in Environmental Genomics (CAREG) Centre for Catalysis Research


id: canadian-university-scientific-research-organizations-20260505-7
file: data/en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations-7.md
category: reference
title: Canadian university scientific research organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Canadian_university_scientific_research_organizations
date_saved: 2026-05-05T08:19:35.071794+00:00
instance: kb-cron
parent: canadian-university-scientific-research-organizations-20260505-0
summary:
=== Health and life sciences === Accel-Rx Health Sciences Accelerator – Accel-Rx (2014–2019) – Vancouver, British Columbia, Aging Gracefully across Environments using Technology to Support Wellness, Engagement and Long Life – AGE-WELL (2014–2019) – Toronto Rehabilitation Institute – University Health Network, Toronto, Ontario, Allergy, Genes and Environment Network – AllerGen (2004–2019) – McMaster University, Hamilton, Ontario, Biotherapeutics for Cancer Treatment – BioCanRx (2014–2019) – Ottawa Hospital Research Institute, Ottawa, Ontario, Canadian Frailty Network – CFN (2012–2017) – Queen's University, Kingston, Ontario, Canadian Glycomics Network – GlycoNet (2014–2019) – University of Alberta, Edmonton, Alberta, Cardiac Arrhythmia Network of Canada – CANet (2014–2019) – Western University, London, Ontario, CellCAN Regenerative Medicine and Cell Therapy Network – CellCAN (2014–2018) – Hôpital Maisonneuve-Rosemont, Montréal, Quebec, Centre for Commercialization of Cancer Immunotherapy – C3i (2016–2021) – Montréal, Quebec, Centre for Commercialization of Regenerative Medicine – CCRM (2011–2017) – Toronto, Ontario, Centre for Drug Research and Development – CDRD (2008–2018) – Vancouver, British Columbia, Centre for Imaging Technology Commercialization – CIMTEC (2011–2018) – London, Ontario, Centre for Probe Development and Commercialization – CPDC (2008–2018) – Hamilton, Ontario, Centre for Surgical Invention and Innovation – CSII (2009–2017) – Hamilton, Ontario, Centre for the Commercialization of Antibodies and


id: canadian-government-scientific-research-organizations-20260505-0
file: data/en.wikipedia.org/wiki/Canadian_government_scientific_research_organizations-0.md
category: reference
title: Canadian government scientific research organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Canadian_government_scientific_research_organizations
date_saved: 2026-05-05T08:19:36.331481+00:00
instance: kb-cron
parent: canadian-government-scientific-research-organizations-20260505-0
summary:
Expenditures by federal and provincial organizations on scientific research and development accounted for about 10% of all such spending in Canada in 2006. These organizations are active in natural and social science research, engineering research, industrial research and medical research. Below is a list of Canadian Federal and Provincial Government scientific research organizations as of January 2008. In some cases the agency mentioned is dedicated exclusively to scientific research, a good example being the National Research Council Canada. In other cases the organization conducts scientific research within the framework of a much larger mandate, such as the transportation research undertaken by the Transportation Development Centre in Montreal which occurs as part on the general transportation regulatory function of Transport Canada. While most of the organizations mentioned here are "brick and mortar", some, such as the Canadian Institutes of Health Research, are "virtual" and consist of dedicated groups of researchers who are geographically dispersed but remain in close contact through electronic means. Total funding for the organizations listed below amounted to about C$2.5 billion in 2006, or about 10% of all scientific research and development spending in Canada. == Federal organizations == === Devoted exclusively to scientific research === Atomic Energy


id: canadian-government-scientific-research-organizations-20260505-1
file: data/en.wikipedia.org/wiki/Canadian_government_scientific_research_organizations-1.md
category: reference
title: Canadian government scientific research organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Canadian_government_scientific_research_organizations
date_saved: 2026-05-05T08:19:36.331481+00:00
instance: kb-cron
parent: canadian-government-scientific-research-organizations-20260505-0
summary:
=== Conducting scientific research in support of a larger mandate === Agriculture and Agri-Food Canada - HQ, Ottawa, Ontario Research organizations Agassiz Research and Development Centre - Agassiz, British Columbia Summerland Research and Development Centre - Summerland, British Columbia Lacombe Research and Development Centre - Lacombe, Alberta Lethbridge Research and Development Centre - Lethbridge, Alberta Saskatoon Research and Development Centre - Saskatoon, Saskatchewan Swift Current Research and Development Centre - Swift Current, Saskatchewan Brandon Research and Development Centre - Brandon, Manitoba Morden Research and Development Centre - Morden, Manitoba London Research and Development Centre - London, Ontario Ottawa Research and Development Centre - Ottawa, Ontario Guelph Research and Development Centre - Guelph, Ontario Harrow Research and Development Centre - Harrow, Ontario Sherbrooke Research and Development Centre - Sherbrooke (Lennoxville Sector), Quebec Saint-Hyacinthe Research and Development Centre - Saint-Hyacinthe, Quebec Quebec Research and Development Centre - Quebec, Quebec Saint-Jean-sur-Richelieu Research and Development Centre - Saint-Jean-sur-Richelieu, Quebec Fredericton Research and Development Centre - Fredericton, New Brunswick Charlottetown Research and Development Centre - Charlottetown, Prince Edward Island Kentville Research and Development Centre - Kentville, Nova Scotia St John's Research and Development Centre - St. John's, Newfoundland and Labrador Canadian Food Inspection Agency -


id: list-of-chemical-engineering-societies-20260505-0
file: data/en.wikipedia.org/wiki/List_of_chemical_engineering_societies-0.md
category: reference
title: List of chemical engineering societies
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_chemical_engineering_societies
date_saved: 2026-05-05T08:19:37.549412+00:00
instance: kb-cron
parent: list-of-chemical-engineering-societies-20260505-0
summary:
This is the list of chemical engineering societies in the world. They are sorted by continent and alphabetically. They include national or international ones, but not student societies or those otherwise restricted to a particular university or institution. == Africa == Ethiopian Society of Chemical Engineers (ESChE), Ethiopia Nigerian Society of Chemical Engineers South African Institution of Chemical Engineers (SAIChE), South Africa == Asia == Asia Pacific Confederation of Chemical Engineering (APCChE) Iranian Association of Chemical Engineering (IAChE) [1], I.R. Iran Indian Institute of Chemical Engineers (IIChe), India [2] Israel Institute of Chemical Engineers (IIChe), Israel [3] Korean Chemical Society (KCS), Korea [4] Korean Institute of Chemical Engineers (ko) (KIChE), Korea [5] Pakistan Institute of Chemical Engineers (PICHE), Pakistan [6] Philippine Institute of Chemical Engineers (PIChE), Philippines [7] Society of Chemical Engineers, Japan (SCEJ) (ja), Japan [8] Society of Chemical Engineers of Nepal, Kathmandu, Nepal [9] Taiwan Institute of Chemical Engineering (TwIChE), Taiwan [10] Thai Institute of Chemical Engineering and Applied Chemistry (TIChE), Thailand [11] == Europe == European Federation of Chemical Engineering (EFCE) (umbrella organization) Associazione Italiana Di Ingegneria Chimica (AIDIC), Italy Chamber of Chemical Engineers, Turkey [12] DECHEMA, Germany Institution of Chemical Engineers (IChemE), UK Société Française de


id: list-of-chemistry-societies-20260505-0
file: data/en.wikipedia.org/wiki/List_of_chemistry_societies-0.md
category: reference
title: List of chemistry societies
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_chemistry_societies
date_saved: 2026-05-05T08:19:38.791225+00:00
instance: kb-cron
parent: list-of-chemistry-societies-20260505-0
summary:
The following is a list of chemistry societies: == A == Alpha Chi Sigma (ΑΧΣ) American Association for Clinical Chemistry American Chemical Society American Crystallographic Association American Institute of Chemical Engineers (AIChE) American Institute of Chemists(AIC) American Oil Chemists' Society American Society of Brewing Chemists American Society for Mass Spectrometry Association of Analytical Communities (AOAC International) Association of Greek Chemists == B == Belgian Society of Biochemistry and Molecular Biology Biochemical Society Brazilian Chemical Society == C == Canadian Society for Chemical Technology (CSCT) Canadian Society of Clinical Chemists - (CSCC) Chemical Abstracts Service (CAS) Chemical Heritage Foundation (CHF), now the Science History Institute Chemical Institute of Canada (CIC) Chemical Society Located in Taipei (CSLT) Chemical Society of Japan (CSJ) Crystallographic Society of Japan (CSJ) Chemical Society of Pakistan Chemical Society of Peru Chinese-American Chemical Society Chinese Chemical Society (Beijing) (CCS) Chinese Chemical Society (Taipei) (CSLT) Council for Chemical Research (CCR) Chemical Research Society of India == D == Danish Chemical Society == E == The Electrochemical Society European Association for Chemical and Molecular Sciences == F == Faraday Society Federation of European Biochemical Societies == G == Gesellschaft Deutscher Chemiker (GDCh) == H == Hungarian Chemical Society == I


id: list-of-computer-science-conferences-20260505-0
file: data/en.wikipedia.org/wiki/List_of_computer_science_conferences-0.md
category: reference
title: List of computer science conferences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_computer_science_conferences
date_saved: 2026-05-05T08:19:40.109147+00:00
instance: kb-cron
parent: list-of-computer-science-conferences-20260505-0
summary:
This is a list of current and past academic conferences in computer science. Only conferences with separate articles are included; within each field, the conferences are listed alphabetically by their short names. == General == FCRC – Federated Computing Research Conference == Algorithms and theory == Conferences accepting a broad range of topics from theoretical computer science, including algorithms, data structures, computability, computational complexity, automata theory and formal languages: CCC - Computational Complexity Conference FCT – International Symposium on Fundamentals of Computation Theory FOCS – IEEE Symposium on Foundations of Computer Science ICALP – International Colloquium on Automata, Languages and Programming ISAAC – International Symposium on Algorithms and Computation STACS – Symposium on Theoretical Aspects of Computer Science STOC – ACM Symposium on Theory of Computing === Algorithms === Conferences whose topic is algorithms and data structures considered broadly, but that do not include other areas of theoretical computer science such as computational complexity theory: ESA – European Symposium on Algorithms SODA – ACM–SIAM Symposium on Discrete Algorithms SWAT and WADS – SWAT and WADS conferences === Geometric algorithms === Conferences on computational geometry, graph drawing, and other application areas of geometric computing: GD – International Symposium on Graph Drawing


id: list-of-computer-science-conferences-20260505-1
file: data/en.wikipedia.org/wiki/List_of_computer_science_conferences-1.md
category: reference
title: List of computer science conferences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_computer_science_conferences
date_saved: 2026-05-05T08:19:40.109147+00:00
instance: kb-cron
parent: list-of-computer-science-conferences-20260505-0
summary:
BTW - GI Conference on Database Systems for Business, Technology and Web ECIR - European Conference on Information Retrieval ECIS - European Conference on Information Systems ER - International Conference on Conceptual Modeling ICDT - International Conference on Database Theory ICIS - International Conference on Information Systems ISWC - International Semantic Web Conference JCDL - ACM/IEEE Joint Conference on Digital Libraries PODS - ACM Symposium on Principles of Database Systems SIGMOD - ACM Special Interest Group on Management of Data WWW - World Wide Web Conference == Artificial intelligence == Conferences on artificial intelligence and machine learning: AAAI - AAAI Conference on Artificial Intelligence AAMAS - International Conference on Autonomous Agents and Multiagent Systems ICAPS - International Conference on Automated Planning and Scheduling CIBB - International Conference on Computational Intelligence Methods for Bioinformatics and Biostatistics ECAI - European Conference on Artificial Intelligence ECML PKDD - European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases ICML - International Conference on Machine Learning ICLR - International Conference on Learning Representations IJCAI - International Joint Conference on Artificial Intelligence ISWC - International Semantic Web Conference NeurIPS - Conference on Neural Information Processing Systems === Evolutionary computation === Conferences


id: list-of-dna-nanotechnology-research-groups-20260505-0
file: data/en.wikipedia.org/wiki/List_of_DNA_nanotechnology_research_groups-0.md
category: reference
title: List of DNA nanotechnology research groups
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_DNA_nanotechnology_research_groups
date_saved: 2026-05-05T08:19:41.392106+00:00
instance: kb-cron
parent: list-of-dna-nanotechnology-research-groups-20260505-0
summary:
This list of DNA nanotechnology research groups gives a partial overview of academic research organisations in the field of DNA nanotechnology, sorted geographically. Any sufficiently notable research group (which in general can be considered as any group having published in well regarded, high impact factor journals) should be listed here, along with a brief description of their research. == North America == == Asia == == Europe == == References ==


id: list-of-food-safety-organisations-20260505-0
file: data/en.wikipedia.org/wiki/List_of_food_safety_organisations-0.md
category: reference
title: List of food safety organisations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_food_safety_organisations
date_saved: 2026-05-05T08:19:42.636722+00:00
instance: kb-cron
parent: list-of-food-safety-organisations-20260505-0
summary:
This is a list of organizations and associated posts which are related to food safety, either as a primary interest or through statutory responsibility. National organizations are grouped by the UN geoscheme. == Africa == Africa Food Safety Forum (AFSF) African Food Safety Network (AFoSaN) The Food Safety and Quality Authority of The Gambia (FSQA) Tanzanian Food and Drugs Authority (TFDA) Ethiopian Food and Drug Authority (EFDA) Moroccan National Office of Food Safety (ONSSA) South African National Regulator for Compulsory Specifications (NRCS) Egyptian Food Safety Authority Ghana Food and Drugs Authority National Agency for Food and Drug Administration and Control Nigerian Food and Drugs Authority National Agency For Food And Drug Administration and Control [1] Kaduna State Livestock Regulatory Authority == Americas == Argentina Minister of Economy Secretariat of Agriculture, Livestock, Fishing and Food National Food Safety and Quality Service (SENASA) Servicio Nacional de Sanidad y Calidad Agroalimentaria Brazil Agência Nacional de Vigilância Sanitária (Anvisa) [2] Canada Minister of Agriculture Agriculture and Agri-Food Canada (AAFC) Canadian Food Inspection Agency (CFIA) Minister of Health Health Canada Health Products and Food Branch Guelph Food Technology Centre (Canada) United States of America U.S. Food and Drug Administration (FDA) Center for Food Safety and


id: list-of-schools-and-organizations-related-to-forensic-entomology-20260505-0
file: data/en.wikipedia.org/wiki/List_of_schools_and_organizations_related_to_forensic_entomology-0.md
category: reference
title: List of schools and organizations related to forensic entomology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_schools_and_organizations_related_to_forensic_entomology
date_saved: 2026-05-05T08:19:43.882414+00:00
instance: kb-cron
parent: list-of-schools-and-organizations-related-to-forensic-entomology-20260505-0
summary:
Forensic entomology is the study of insects related to humans. There are three areas associated with forensic entomology: urban entomology, stored products entomology, and mediocriminal entomology. This list concerns only the area of mediocriminology and the schools and organizations associated with it. Mediocriminology is the interaction of the criminal justice system and the use of insects for investigations pertaining to the deaths of humans. This is a growing science in which nations around the world are partaking in research to expand its applications. The following list of schools and organizations is not comprehensive due to the ever-changing nature of forensic entomology. == Schools == === Texas A&M University === Texas A&M University's Entomology Department announced the Forensic and Investigative Science Program November 23, 2007 as a means to prepare students to address and solve problems through the use of various techniques, including forensic entomology. This program offers the first B.S. in this field in Texas. The staff consists of several professors and lecturers, most notably Dr. Jeff Tomberlin, assistant professor since fall 2007 and member of the American Board of Forensic Entomology Certified Entomologists and University of Georgia graduate with a Ph.D. in entomology. Another noteworthy entomologist at Texas A&M


id: list-of-schools-and-organizations-related-to-forensic-entomology-20260505-1
file: data/en.wikipedia.org/wiki/List_of_schools_and_organizations_related_to_forensic_entomology-1.md
category: reference
title: List of schools and organizations related to forensic entomology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_schools_and_organizations_related_to_forensic_entomology
date_saved: 2026-05-05T08:19:43.882414+00:00
instance: kb-cron
parent: list-of-schools-and-organizations-related-to-forensic-entomology-20260505-0
summary:
=== Australian Entomological Society === The Australian Entomological Society (AES) now with more than six hundred members, is one of the most prevalent biological science organizations in Australia. AES began August 17, 1965 and had its first public meeting in Melbourne in January 1967. The meeting was coordinated by Ian Mackerras, who put forth four important goals to inspire the success of the AES, these goals included: "Acquiring wealth, setting a high attainable standard of excellence, having a clear central purpose and source of inspiration, and finally existing as a group for what the group can give back to society, not what it can get" (from the AES Website).Now led by current president Phil Weinstein (2017), AES members consists of about seventy-five percent professionals and around twenty five percent amateurs. Membership is not restricted to any one person they just have to be interested in the study of insects. A person must also gain two nominations by financial members to finally be inducted into the group. The AES includes a number of affiliates such as, The Entomological Society of Queensland, The entomological Society of New South Wales, and The Entomological Society of Victoria. The AES also consists of business firms


id: list-of-schools-and-organizations-related-to-forensic-entomology-20260505-2
file: data/en.wikipedia.org/wiki/List_of_schools_and_organizations_related_to_forensic_entomology-2.md
category: reference
title: List of schools and organizations related to forensic entomology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_schools_and_organizations_related_to_forensic_entomology
date_saved: 2026-05-05T08:19:43.882414+00:00
instance: kb-cron
parent: list-of-schools-and-organizations-related-to-forensic-entomology-20260505-0
summary:
=== European Association for Forensic Entomology === EAFE, European Association for Forensic Entomology, was founded in 2002 and vastly growing in size. There are close to about 100 members and 41 associate members. The aim of EAFE is to encourage the advancement of forensic entomology all through Europe and to encourage co-operation with related international bodies. According to EAFE, “This growth reflects the growing interest by the forensic and entomological community in forensic entomology, but at the same time highlights the need for guidelines for the science and support for it from an association like EAFE". EAFE provides its services as a professional partner for police and legal authorities. EAFE holds regular meetings and workshops in order to raise awareness and knowledge of their science. The annual meeting are held in order to advance education and training, as well as to fine tune the framework of the association i.e. Constitution, membership, etc. In order to become a member of EAFE one must meet certain criteria such as their profession. You must be a qualified scientist, pathologist or someone with a medical or forensic background who is readily active in the field of entomology. One must also be within the EU.


id: list-of-genetics-research-organizations-20260505-0
file: data/en.wikipedia.org/wiki/List_of_genetics_research_organizations-0.md
category: reference
title: List of genetics research organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_genetics_research_organizations
date_saved: 2026-05-05T08:19:45.290288+00:00
instance: kb-cron
parent: list-of-genetics-research-organizations-20260505-0
summary:
This is a list of organizations involved in genetics research. == Africa == === Kenya === International Livestock Research Institute (ILRI), Nairobi === Namibia === The Life Technologies Conservation Genetics Laboratory (Cheetah Conservation Fund), Otjiwarongo == Asia == === Malaysia === Malaysian Genomics Resource Centre (MGRC) Genetics & Regenerative Medicine Research Centre (GRMRC) Malaysia Genome and Vaccine Institute (MGVI) Medical Genetics Unit, Universiti Putra Malaysia === Pakistan === IBGE Institute of Biomedical and Genetic Engineering === China === BGI Group Chinese National Human Genome Center === India === Institute of Genomics and Integrative Biology DNA Labs India National Institute of Biomedical Genomics === Iran === Royan Institute === Philippines === Philippine Genome Center International Rice Research Institute === Singapore === Genome Institute of Singapore Institute of Molecular and Cell Biology === Taiwan === National Health Research Institutes === Japan === National Institute of Genetics Okinawa Institute of Science and Technology RIKEN === United Arab Emirates === DNA Labs UAE == Europe == === Germany === Max Planck Institute for Molecular Genetics === Italy === Bioversity International === Sweden === Science for Life Laboratory === United Kingdom === The Genome Analysis Centre Wellcome Sanger Institute Wellcome Centre for Human Genetics (University


id: list-of-geographical-societies-20260505-0
file: data/en.wikipedia.org/wiki/List_of_geographical_societies-0.md
category: reference
title: List of geographical societies
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_geographical_societies
date_saved: 2026-05-05T08:19:46.580100+00:00
instance: kb-cron
parent: list-of-geographical-societies-20260505-0
summary:
This is a list of geographical societies. == International == EUGEO-Association of Geographical Societies in Europe EUROGEO-European Association of Geographers European Geography Association Gamma Theta Upsilon International Geographical Union World Geographers Association == Australia == Royal Geographical Society of Queensland Royal Geographical Society of South Australia == Belgium == Société Royale Belge de Géographie == Canada == Canadian Association of Geographers Royal Canadian Geographical Society == Egypt == Egyptian Geographic Society == France == Société de Géographie == Germany == Gesellschaft für Erdkunde zu Berlin == Hong Kong == Hong Kong Critical Geography Group Hong Kong Geographical Association == Italy == Società Geografica Italiana == Mexico == Sociedad Mexicana de Geografía y Estadística == Netherlands == Royal Dutch Geographical Society == Norway == Norwegian Geographical Society == Peru == Geographical Society of Lima == Portugal == Lisbon Geographic Society == Russia == Russian Geographical Society == Saudi Arabia == Saudi Geographical Society == Slovenia == Association of Slovenian Geographers == United Kingdom == Geographical Association Royal Geographical Society Royal Scottish Geographical Society == United States == American Geographical Society Association of American Geographers Association of Pacific Coast Geographers Illinois Geographical Society National Council for Geographic Education National Geographic Society Society


id: list-of-geoscience-organizations-20260505-0
file: data/en.wikipedia.org/wiki/List_of_geoscience_organizations-0.md
category: reference
title: List of geoscience organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_geoscience_organizations
date_saved: 2026-05-05T08:19:47.828029+00:00
instance: kb-cron
parent: list-of-geoscience-organizations-20260505-0
summary:
This is a list of geoscience organizations, including such fields of geosciences as geology, geophysics, hydrology, oceanography, petrophysics, and related fields. == Intercontinental organizations == Anthropocene Working Group Association for Women Geoscientists (AWG) Association of Applied Geochemists Environmental and Engineering Geophysical Society Geochemical Society International Association for Engineering Geology and the Environment International Association for Mathematical Geosciences (IAMG) International Association of Cryospheric Sciences International Association of GeoChemistry International Association of Geomagnetism and Aeronomy International Association of Hydrological Sciences (IAHS/AISH) International Association of Volcanology and Chemistry of the Earth's Interior (IAVCEI) – International non-governmental organization International Association for the Conservation of Geological Heritage ProGEO International Centre for Diffraction Data International Commission on Stratigraphy (ICS) – Non-governmental geological organization International Commission on the History of Geological Sciences International Continental Scientific Drilling Program International Geoscience Programme International Glaciological Society (IGS) – International glaciology academic organization International Mineralogical Association International Organization for Biological Crystallization International Permafrost Association International Union for Quaternary Research International Union of Crystallography International Union of Geodesy and Geophysics (IUGG) – International non-governmental organization International Union of Geological Sciences (IUGS) – International non-governmental organization Geoscience Education, Training and Technology Transfer International Union of Soil Sciences (IUSS) – International scientific union OneGeology


id: list-of-geoscience-organizations-20260505-1
file: data/en.wikipedia.org/wiki/List_of_geoscience_organizations-1.md
category: reference
title: List of geoscience organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_geoscience_organizations
date_saved: 2026-05-05T08:19:47.828029+00:00
instance: kb-cron
parent: list-of-geoscience-organizations-20260505-0
summary:
=== United States === American Association of Petroleum Geologists (AAPG) – Professional geological association American Crystallographic Association American Gem Society (AGS), also known as American Gemological Society – American trade association American Geosciences Institute (AGI) – Nonprofit scientific federation American Geophysical Union (AGU) – Nonprofit organization of geophysicists American Institute of Mining, Metallurgical, and Petroleum Engineers, also known as Society for Mining, Metallurgy, and Exploration (SME) American Quaternary Association Association for the Sciences of Limnology and Oceanography (ASLO), also known as American Society of Limnology and Oceanography Association of Environmental & Engineering Geologists (AEG) The Clay Minerals Society (CMS) – US-based non-profit organizationPages displaying short descriptions of redirect targets Earth Science Women's Network (ESWN) Environmental and Engineering Geophysical Society (EEGS) Gemological Institute of America (GIA) – Research institute in Carlsbad, California Geological Society of America (GSA) – Nonprofit organization dedicated to geoscience Geoscience Information Society (GSIS) Keck Geology Consortium Lamont–Doherty Earth Observatory Mineralogical Society of America (MSA) – Scientific organization promoting mineralogy National Association of Black Geologists and Geophysicists (NABGG) National Center for Earth-surface Dynamics National Cooperative Soil Survey (NCSS) – Program to understand and manage US soils National Speleological Society (NSS) – Organization for exploration, conservation, and study of


id: list-of-scientific-bodies-explicitly-rejecting-intelligent-design-20260505-0
file: data/en.wikipedia.org/wiki/List_of_scientific_bodies_explicitly_rejecting_intelligent_design-0.md
category: reference
title: List of scientific bodies explicitly rejecting intelligent design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_scientific_bodies_explicitly_rejecting_intelligent_design
date_saved: 2026-05-05T08:19:49.158508+00:00
instance: kb-cron
parent: list-of-scientific-bodies-explicitly-rejecting-intelligent-design-20260505-0
summary:
This article lists those scientific organisations and other nationally or internationally recognised groups that specifically reject intelligent design as a valid alternative to evolutionary theory. == United States ==


id: list-of-scientific-bodies-explicitly-rejecting-intelligent-design-20260505-1
file: data/en.wikipedia.org/wiki/List_of_scientific_bodies_explicitly_rejecting_intelligent_design-1.md
category: reference
title: List of scientific bodies explicitly rejecting intelligent design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_scientific_bodies_explicitly_rejecting_intelligent_design
date_saved: 2026-05-05T08:19:49.158508+00:00
instance: kb-cron
parent: list-of-scientific-bodies-explicitly-rejecting-intelligent-design-20260505-0
summary:
=== National === The American Association for the Advancement of Science is the world's largest general scientific society. The AAAS serves some 262 affiliated societies and academies of science, serving 10 million individuals. A 2002 statement states: "[T]he lack of scientific warrant for so-called 'intelligent design theory' makes it improper to include as a part of science education." A 2006 statement on the teaching of evolution: "Some bills seek to discredit evolution by emphasizing so-called "flaws" in the theory of evolution or "disagreements" within the scientific community. Others insist that teachers have absolute freedom within their classrooms and cannot be disciplined for teaching non-scientific "alternatives" to evolution. A number of bills require that students be taught to "critically analyze" evolution or to understand "the controversy." But there is no significant controversy within the scientific community about the validity of the theory of evolution. The current controversy surrounding the teaching of evolution is not a scientific one." Q & A on Evolution and Intelligent Design: Is intelligent design a scientific alternative to contemporary evolutionary theory? No. Intelligent design proponents may use the language of science, but they do not use its methodology. They have yet to propose meaningful tests for their


id: list-of-scientific-bodies-explicitly-rejecting-intelligent-design-20260505-2
file: data/en.wikipedia.org/wiki/List_of_scientific_bodies_explicitly_rejecting_intelligent_design-2.md
category: reference
title: List of scientific bodies explicitly rejecting intelligent design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_scientific_bodies_explicitly_rejecting_intelligent_design
date_saved: 2026-05-05T08:19:49.158508+00:00
instance: kb-cron
parent: list-of-scientific-bodies-explicitly-rejecting-intelligent-design-20260505-0
summary:
Underlying both of these concepts, and foundational to IDC itself, is an early 19th-century British theological view, the 'argument from design.'" The NCSE also maintains lists of organizations from around the world that oppose the teaching of creationism, including intelligent design, listing 71 scientific organizations, 23 religious organizations, 43 educational organizations, and 10 civil liberties organizations. The National Science Teachers Association NSTA is a professional association of 55,000 science teachers and administrators. "We stand with the nation's leading scientific organizations and scientists, including Dr. John Marburger, the president's top science advisor, in stating that intelligent design is not science. … It is simply not fair to present pseudoscience to students in the science classroom." United States National Academy of Sciences The academy wrote a statement entitled "Science and Creationism: A View from the National Academy of Sciences, Second Edition National Academy of Sciences" which said that "Creationism, Intelligent Design, and other claims of supernatural intervention in the origin of life or of species are not science". There was also a letter from Bruce Alberts, former president, NAS: "We stand ready to help others in addressing the increasingly strident attempts to limit the teaching of evolution or to introduce non-scientific 'alternatives'


id: list-of-scientific-bodies-explicitly-rejecting-intelligent-design-20260505-3
file: data/en.wikipedia.org/wiki/List_of_scientific_bodies_explicitly_rejecting_intelligent_design-3.md
category: reference
title: List of scientific bodies explicitly rejecting intelligent design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_scientific_bodies_explicitly_rejecting_intelligent_design
date_saved: 2026-05-05T08:19:49.158508+00:00
instance: kb-cron
parent: list-of-scientific-bodies-explicitly-rejecting-intelligent-design-20260505-0
summary:
=== State and university === Kentucky Academy of Science states "...in the strongest and most determined ways possible deplores the decision to substitute "change over time" for "evolution" in the state teaching standards, urges that the original wording be reinstated, and decries any attempt to remove the teaching of basic evolutionary theory..." Adopted by KAS Governing Board November 6, 1999. Passed unanimously by KAS membership November 6, 1999. Unanimously approved again at its annual business meeting on November 11, 2005. The KAS also voted to endorse the October 2002 AAAS Board Resolution on Intelligent Design Theory. The Kentucky Paleontological Society Statement on Teaching Evolution states that "KPS is opposed to any attempt to teach creationism or omit mention of evolution from public school instruction. Furthermore, evolution should be called "evolution" in curriculum guidelines and other documents; euphemisms such as "change over time" are intellectually dishonest for they attempt to conceal the terminology used by scientists." Executive Committee approved this statement in 1999. The Lehigh University Department of Biological Sciences responded to faculty member and intelligent design proponent Michael Behe's claims about the scientific validity and usefulness of intelligent design, publishing an official position statement which says "It is our collective


id: list-of-mathematical-societies-20260505-0
file: data/en.wikipedia.org/wiki/List_of_mathematical_societies-0.md
category: reference
title: List of mathematical societies
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_mathematical_societies
date_saved: 2026-05-05T08:19:50.447528+00:00
instance: kb-cron
parent: list-of-mathematical-societies-20260505-0
summary:
This article provides a list of mathematical societies. == International == African Mathematical Union Association for Women in Mathematics Circolo Matematico di Palermo European Mathematical Society European Women in Mathematics Foundations of Computational Mathematics International Association for Cryptologic Research International Association of Mathematical Physics International Linear Algebra Society International Mathematical Union International Society for Analysis, its Applications and Computation International Society for Mathematical Sciences International Statistical Institute Kurt Gödel Society Mathematical Council of the Americas (MCofA) Mathematical Optimization Society Mathematical Society of South Eastern Europe (MASSEE) Quaternion Association Ramanujan Mathematical Society Society for Industrial and Applied Mathematics Southeast Asian Mathematical Society (SEAMS) Spectra (mathematical association) Unión Matemática de América Latina y el Caribe (UMALCA) Young Mathematicians Network == Honor societies == Kappa Mu Epsilon Mu Alpha Theta Pi Mu Epsilon == National and subnational == This list is sorted by continent. Country and/or subregion/city is given if not specified in name. === Africa === Algeria Mathematical Society Gabon Mathematical Society South African Mathematical Society === Asia === Bangladesh Mathematical Society Calcutta Mathematical Society, Kolkata, India Chinese Mathematical Society Indian Mathematical Society Iranian Mathematical Society Israel Mathematical Union Kerala Mathematical Association, Kerala State, India Korean Mathematical Society, South Korea Mathematical Society


id: list-of-meteorology-institutions-20260505-0
file: data/en.wikipedia.org/wiki/List_of_meteorology_institutions-0.md
category: reference
title: List of meteorology institutions
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_meteorology_institutions
date_saved: 2026-05-05T08:19:51.693924+00:00
instance: kb-cron
parent: list-of-meteorology-institutions-20260505-0
summary:
The following is a list of meteorology institutions around the world. == Governmental == === Africa === Egyptian Meteorological Authority Ghana Meteorological Agency Mozambique National Institute of Meteorology National Meteorological Office ONM (Algeria) South African Weather Service SAWS === Americas === Canada Environment and Climate Change Canada Meteorological Service of Canada Canadian Ice Service Canadian Meteorological Centre United States: National Center for Atmospheric Research NCAR National Oceanic and Atmospheric Administration NOAA National Severe Storms Laboratory National Climatic Data Center National Weather Service National Centers for Environmental Prediction National Hurricane Center Storm Prediction Center Naval Maritime Forecast Center/Joint Typhoon Warning Center Bermuda Weather Service Instituto Nacional de Meteorologia (Brazil) Institute of Hydrology, Meteorology and Environmental Studies (Colombia) Instituto Meteorológico Nacional (Costa Rica) Institute of Meteorology (Cuba) Instituto Nacional Meteorologia e Hidrologia (Ecuador) Instituto Nacional de Sismología, Vulcanología, Meteorología e Hidrología (Guatemala) Instituto Nacional De Meteorologia E Hidrologia (Venezuela) National Service of Meteorology and Hydrology of Peru Servicio Meteorológico Nacional (Argentina) Servicio Meteorológico Nacional (Mexico) Uruguayan Institute of Meteorology === Asia / Oceania === Afghanistan Meteorological Department Bureau of Meteorology (Australia) Bangladesh Meteorological Department BMD Central Weather Administration (Taiwan) China Meteorological Administration CMA Hong Kong Observatory HKO Macao Meteorological and Geophysical Bureau


id: ministry-of-science-20260505-0
file: data/en.wikipedia.org/wiki/Ministry_of_science-0.md
category: reference
title: Ministry of science
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ministry_of_science
date_saved: 2026-05-05T08:20:04.763411+00:00
instance: kb-cron
parent: ministry-of-science-20260505-0
summary:
A science ministry or department of science is a ministry or other government agency responsible for governing scientific activities. The ministry is often headed by a minister specialising in scientific matters. == List of ministries of science == Many countries have a ministry of science or ministry of science and technology: Ministry of Science, Technology and Productive Innovation (Argentina) Ministry of Science and Technology (Bangladesh) Ministry of Science, Technology and Innovation (Brazil) Innovation, Science and Economic Development Canada Ministry of Science, Technology, Knowledge and Innovation (Chile) Ministry of Science and Technology (China) Ministry of Science, Technology and Environment (Cuba) Ministry of Science, Technology and Innovation of Denmark Ministry of Higher Education, Science and Culture (East Timor) Federal Ministry of Education and Research (Germany) Ministry of Education, Science and Culture (Iceland) Ministry of Science and Technology (India) Ministry of Higher Education, Science, and Technology (Indonesia) Ministry of Science, Research and Technology (Iran) Department of Further and Higher Education, Research, Innovation and Science (Ireland) Ministry of Education, Culture, Sports, Science and Technology (Japan) Ministry of Education and Science (Lithuania) Ministry of Science and Technology (Malaysia) Ministry of Education and Science (Mongolia) Ministry of Science and Technology (Myanmar) Ministry of Education and Science


id: list-of-science-museums-20260505-0
file: data/en.wikipedia.org/wiki/List_of_science_museums-0.md
category: reference
title: List of science museums
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_science_museums
date_saved: 2026-05-05T08:20:06.030683+00:00
instance: kb-cron
parent: list-of-science-museums-20260505-0
summary:
Below is a list of science museums all over the world. See Science museum for definitions. == Europe == === Austria === Ars Electronica Center, Linz Haus der Musik (House of Music), Vienna Naturhistorisches Museum Wien (Natural History Museum), Vienna Technisches Museum Wien (Vienna Technical Museum), Vienna === Belgium === Euro Space Center, Libin Hidrodoe, Herentals Pass, Frameries Royal Belgian Institute of Natural Sciences, Brussels Technopolis, Mechelen === Bulgaria === National Polytechnical Museum, Sofia === Croatia === Nikola Tesla Memorial Center, Smiljan Split Science Museum and Zoo, Split Technical Museum, Zagreb === Czech Republic === National Technical Museum, Prague Techmania Science Center, Plzeň === Denmark === Kroppedal, Copenhagen Natural History Museum of Denmark, Copenhagen Science Museums, Aarhus Tycho Brahe Planetarium, Copenhagen === Estonia === AHHAA, Tartu === Finland === Arktikum, Rovaniemi Heureka, Vantaa Tietomaa, Oulu === France === Ampère Museum, Lyon Cité de l'espace, Toulouse Cité des Sciences et de l'Industrie, Paris Micropolis (La Cité des Insectes), Millau Musée des Arts et Métiers, Paris Palais de la Découverte, Paris Vulcania, Saint-Ours-les-Roches Exploradôme, Vitry-sur-Seine === Germany === Deutsches Museum, Munich experimenta, Heilbronn German Hygiene Museum, Dresden German Museum of Technology (Berlin) Hermann Oberth Space Travel Museum, Feucht, Bavaria Mathematikum, Gießen Mathematisch-Physikalischer


id: list-of-science-museums-20260505-1
file: data/en.wikipedia.org/wiki/List_of_science_museums-1.md
category: reference
title: List of science museums
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_science_museums
date_saved: 2026-05-05T08:20:06.030683+00:00
instance: kb-cron
parent: list-of-science-museums-20260505-0
summary:
=== China === China Science and Technology Museum, Beijing Beijing Museum of Natural History Shanghai Science and Technology Museum, Pudong, Shanghai Sichuan Science and Technology Museum, Sichuan Guangdong Science Center, Guangzhou === Hong Kong === Health Education Exhibition and Resource Centre, Kowloon Park Hong Kong Museum of Medical Sciences, Mid-Levels Fanling Environmental Resource Centre, Fanling Hong Kong Science Museum, Tsim Sha Tsui Hong Kong Space Museum, Tsim Sha Tsui Jockey Club Museum of Climate Change, New Territories === India === Birla Industrial & Technological Museum, Kolkata Birla Science Museum, Hyderabad Gujarat Science City, Ahmedabad Birla Planetarium, Chennai Hakim Karam Hussain Museum on History of Medicine and Sciences Kerala Science and Technology Museum, Thiruvananthapuram National Council of Science Museums (NCSM) National Science Centre, Delhi Nehru Museum of Science and Technology, Kharagpur Nehru Science Centre, Mumbai Regional Science Centre, Bhopal Science City Kolkata, Kolkata Science Park, Jaipur Srikrishna Science Centre, Patna Visvesvaraya Industrial and Technological Museum, Bangalore === Indonesia === Bandung Geological Museum, Bandung Puspa Iptek Sundial, Bandung Bogor Zoology Museum, Bogor Jakarta Planetarium and Observatory, Taman Ismail Marzuki, Jakarta Taman Pintar Yogyakarta, Yogyakarta === Iran === Iran National museum of science and technology, Tehran === Israel === Bloomfield Science Museum, Jerusalem


id: list-of-nanotechnology-organizations-20260505-0
file: data/en.wikipedia.org/wiki/List_of_nanotechnology_organizations-0.md
category: reference
title: List of nanotechnology organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_nanotechnology_organizations
date_saved: 2026-05-05T08:20:07.294375+00:00
instance: kb-cron
parent: list-of-nanotechnology-organizations-20260505-0
summary:
This is a list of organizations involved in nanotechnology. == Government == === Brazil === Brazilian Nanotechnology National Laboratory === China === National Center for Nanoscience and Technology === Canada === National Institute for Nanotechnology Waterloo Institute for Nanotechnology === European Union === EU Seventh Framework Programme Action Plan for Nanosciences and Nanotechnologies 2005-2009 === India === MEMS, Microfluidics and Nanoelectronics Lab (BITS Pilani) Centre for Nanotechnology Research (Vellore Institute of Technology) Institute of Nano Science and Technology Indian Nano-Biologist Association Centre for Nano and Soft Matter Sciences Indian Association for the Cultivation of Science S. N. Bose National Centre for Basic Sciences National Chemical Laboratory Jawaharlal Nehru Centre for Advanced Scientific Research Saha Institute of Nuclear Physics Center For Converging Technologies (University of Rajasthan) Center For Nano Science and Engineering (Indian Institute of Science) Special Centre for Nano Sciences (Jawaharlal Nehru University) Centre for Nanoscience and Nanotechnology (Jamia Millia Islamia) Department of Nano Science and Technology (Tamil Nadu Agricultural University) Department of Nanotechnology (University of Kashmir) Parul University Micro-Nano Research & Development Center (Parul University) === Iran === Iranian Nanotechnology Laboratory Network Iran Nanotechnology Initiative Council (INIC) === Ireland === Collaborative Centre for Applied Nanotechnology === Russia === Russian


id: list-of-nanotechnology-organizations-20260505-1
file: data/en.wikipedia.org/wiki/List_of_nanotechnology_organizations-1.md
category: reference
title: List of nanotechnology organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_nanotechnology_organizations
date_saved: 2026-05-05T08:20:07.294375+00:00
instance: kb-cron
parent: list-of-nanotechnology-organizations-20260505-0
summary:
==== Switzerland ==== Swiss Nanoscience Institute (SNI) ==== United Kingdom ==== Bristol Centre for Functional Nanomaterials at University of Bristol London Centre for Nanotechnology James Watt Nanofabrication Centre at University of Glasgow Manufacturing Engineering Centre at Cardiff University Nanoscale Science & Nanotechnology Group at Newcastle University Southampton Nanofabrication Centre at University of Southampton === Asia === ==== India ==== Institute of Nano Science and Technology Deenbandhu Chhotu Ram University of Science and Technology Srinivas Institute of Technology Centre for Nano and Soft Matter Sciences Centre for Nano Science and Engineering, Indian Institute of Science Nano-Materials Research Lab, Tata Institute of Fundamental Research Center for Excellence in Nano-Electronics, Department of Electrical Engineering, IIT Bombay Nanoscale Research Facility, IIT Delhi Sophisticated Analytical Instrumentation Facility, DST Unit of Nanoscience, IIT Madras Thematic Unit of Excellence, IIT Kanpur K.B Chandrashekar Centre for Nanoscience and Technology, Anna University Department of Physics, Banaras Hindu University Department of Technology, Savitribai Phule Pune University Centre for Research in Nanoscience and Nanotechnology, University of Calcutta National Centre for Nanoscience and Nanotechnology, University of Madras School Of Material Science and Nanotechnology, Jadavpur University Nanotechnology Research Center, SRM University Centre for Nanotechnology Research, VIT University Amrita Centre for Nanoscience and Molecular


id: list-of-physics-conferences-20260505-0
file: data/en.wikipedia.org/wiki/List_of_physics_conferences-0.md
category: reference
title: List of physics conferences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_physics_conferences
date_saved: 2026-05-05T08:20:08.439068+00:00
instance: kb-cron
parent: list-of-physics-conferences-20260505-0
summary:
This is a list of academic conferences in physics and astronomy. == On specific lectures == This section includes only events that have a link within Wikipedia 1959 Richard Feynman's There's Plenty of Room at the Bottom, American Physical Society meeting == On singular or limited events == This section includes only events that have a link within Wikipedia 1798 European congress of astronomers 1900 International Congress of Physics 1927 Como Conference 1935–1947 Washington Conferences on Theoretical Physics 1947 Shelter Island Conference 1948 Pocono Conference 1949 Oldstone Conference 1952–1958 Sherwood conferences by Project Sherwood 1959 Chapel Hill Conference 1987 American Physical Society meeting, also known as the Woodstock of physics == Recurring events == European Conference on the Dynamics of Molecular Systems International Colloquium on Group Theoretical Methods in Physics International Conference of Laser Applications by the Society for Optical and Quantum Electronics International Conference of Physics Students by the International Association of Physics Students (IAPS) International Conference on Cold Fusion Defects in Semiconductors Differential Geometric Methods in Theoretical Physics Electronic Properties of Two-Dimensional Systems High Energy Physics, by the International Union of Pure and Applied Physics (IUPAP), also known as the Rochester Conferences Low Temperature Physics by the IUPAP


id: list-of-science-parks-in-the-united-kingdom-20260505-0
file: data/en.wikipedia.org/wiki/List_of_science_parks_in_the_United_Kingdom-0.md
category: reference
title: List of science parks in the United Kingdom
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_science_parks_in_the_United_Kingdom
date_saved: 2026-05-05T08:20:11.080228+00:00
instance: kb-cron
parent: list-of-science-parks-in-the-united-kingdom-20260505-0
summary:
This is a list of science parks in the United Kingdom. == England == === South West === Bristol and Bath Science Park – Emersons Green, Bristol Electronics & Photonics Innovation Centre (EPIC) – Paignton, Devon Exeter Science Park – Exeter Future Space – Stoke Gifford, Bristol Plymouth Science Park – Plymouth Porton Down – Porton, Wiltshire Dorset Innovation Park – Winfrith, Dorset === South East === Begbroke Science Park – Begbroke, near Oxford Culham Science Centre – Culham, Oxfordshire Discovery Park – Sandwich, Kent Harwell Science and Innovation Campus – Harwell, Oxfordshire Kent Science Park – Sittingbourne Langstone Technology Park – Havant, Hampshire Milton Park – South Oxfordshire Oxford Science Park – Oxford Surrey Research Park – Guildford University of Reading Science & Technology Centre – Reading Southampton Science Park – Southampton === Greater London === Brunel Science Park – Uxbridge Lee Valley Technopark – Tottenham South Bank Technopark – Southwark The London Science Park at The Bridge – Dartford === East Anglia === Allia Future Business Centre – Cambridge, Peterborough and East London Babraham Research Campus – Cambridge BioPark – Welwyn Garden City Cambridge Research Park – Cambridge Cambridge Science Park – Cambridge Cambridge Bio-Medical Campus – Cambridge


id: list-of-systems-sciences-organizations-20260505-0
file: data/en.wikipedia.org/wiki/List_of_systems_sciences_organizations-0.md
category: reference
title: List of systems sciences organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_systems_sciences_organizations
date_saved: 2026-05-05T08:20:13.603964+00:00
instance: kb-cron
parent: list-of-systems-sciences-organizations-20260505-0
summary:
Systems science is the interdisciplinary field of science surrounding systems theory, cybernetics, the science of complex systems. It aims to develop interdisciplinary foundations, which are applicable in a variety of areas, such as engineering, biology, medicine and social sciences. Systems science and systemics are names for all research related to systems theory. It is defined as an emerging branch of science that studies holistic systems and tries to develop logical, mathematical, engineering and philosophical paradigms and frameworks in which physical, technological, biological, social, cognitive and metaphysical systems can be studied and developed. This list of systems sciences organizations gives an overview of global and local organizations in the field of systems science. This list shows all kinds of organizations and institutes listed thematically. == Awards == Richard E. Bellman Control Heritage Award George B. Dantzig Prize Donald P. Eckman Award IEEE Simon Ramo Medal: award for exceptional achievement in systems engineering and systems science John von Neumann Theory Prize Rufus Oldenburger Medal A. M. Turing Award UKSS Gold Medallists by the United Kingdom Systems Society The Hellenic Society for Systemic Studies Medal Senior Researcher Award of the Complex Systems Society == Research centers == === General === ==== America ====


id: list-of-technology-centers-20260505-0
file: data/en.wikipedia.org/wiki/List_of_technology_centers-0.md
category: reference
title: List of technology centers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_technology_centers
date_saved: 2026-05-05T08:20:15.012774+00:00
instance: kb-cron
parent: list-of-technology-centers-20260505-0
summary:
This is a list some of technology centers throughout the world. Government planners and business networks often incorporate "silicon" or "valley" into place names to describe their own areas as a result of the success of Silicon Valley in California. Metrics may be applied to measure qualitative differences between these places, including: How much and to what extent public and/or private research and development (R&D) funds are spent in the zones What percentage of local employment is technology related If the zone is mainly government funded or is mainly corporate driven (or is it a mix of both) If mainly corporate, how much revenue and profit and which corporations have headquarters there If mainly corporate, how much venture capital has been made available to companies in the zone What supporting higher educational institutions (e.g., universities or colleges) are located nearby == Globally prominent clusters == Silicon Valley: Originating in Stanford University (Palo Alto and Menlo Park), and spreading south towards San Jose, California, and suburbs. San Francisco and nearby areas including Berkeley and Oakland are technically not part of Silicon Valley but have seen growth in industries such as web development since the 90s and venture capital. Silicon Valley, home


id: list-of-technology-centers-20260505-1
file: data/en.wikipedia.org/wiki/List_of_technology_centers-1.md
category: reference
title: List of technology centers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_technology_centers
date_saved: 2026-05-05T08:20:15.012774+00:00
instance: kb-cron
parent: list-of-technology-centers-20260505-0
summary:
=== Americas === Bolivia Urubó (Santa Cruz de la Sierra) Brazil Florianópolis Campinas, São Paulo, São José dos Campos, São Carlos: The Silicon Valley of Brazil Porto Digital: Recife Porto Alegre TecnoPuc: Porto Alegre BH – São Pedro Valley: Belo Horizonte Parque Tecnológico Aberto de Santa Rita do Sapucaí: Santa Rita do Sapucaí Parque Científico e Tecnológico da UNICAMP: Campinas Feevale Techpark: Porto Alegre ORION Parque Tecnológico: Lages Parque Tecnológico Botucatu: Botucatu Parque Tecnológico UFRJ: Rio de Janeiro Parque Tecnológico da Bahia: Salvador Parque de Desenvolvimento Tecnológico Universidade Federal do Ceará: Fortaleza Sergipe Parque Tecnológico: São Cristóvão Fundação Parque Tecnológico da Paraíba: Campina Grande Canada Canada's Technology Triangle with Kitchener-Waterloo, Ontario: home to BlackBerry (formerly Research in Motion), Open Text, Kik Messenger, Desire2Learn, and the Canadian head office of Google; home to the Communitech HUB start-up incubator Greater Vancouver, British Columbia: home to Sony Pictures Imageworks, PMC-Sierra, Telus, Hootsuite, EA Canada, Vision Critical, MacDonald, Dettwiler and Associates, Westport Innovations, Slack Technologies, Teradici and D-Wave Systems Silicon Valley North: the National Capital Region around Ottawa, Ontario, Bayview Yards,—home to Mitel, Shopify, DragonWave, Alcatel Lucent, and Halogen Software Markham, Ontario: home to the Canadian head offices of Sony, Avaya, IBM, Motorola, Toshiba,


id: list-of-technology-centers-20260505-2
file: data/en.wikipedia.org/wiki/List_of_technology_centers-2.md
category: reference
title: List of technology centers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_technology_centers
date_saved: 2026-05-05T08:20:15.012774+00:00
instance: kb-cron
parent: list-of-technology-centers-20260505-0
summary:
Singapore Singapore Science Park: Southwestern Singapore South Korea Daedeok Science Town, Daejeon Digital Media City, Seoul LG Science Park, Seoul Pangyo Techno Valley, Gyeonggi Samsung Town, Seoul Gumi Technology Industrial Park, Gumi, North Gyeongsang Pohang University of Science and Technology, Pohang, North Gyeongsang Changwon Industrial Park, South Gyeongsang Ulsan technological park, South Gyeongsang Songdo, Incheon, Gyeonggi-do Teheran Valley, Seoul Taiwan Central Taiwan Science Park: Changhua County, Nantou County, Taichung City and Yunlin County Southern Taiwan Science Park: Kaohsiung City and Tainan City Nankang Software Park: Taipei City Neihu High Tech Science Park: Taipei City Hsinchu Science Park: Hsinchu City Thailand Thailand Science Park, north of Bangkok Software Park Thailand, Bangkok Uzbekistan IT-Park, Tashkent Vietnam Hoa Lac Hi-tech Park, Hanoi Saigon Hi-Tech Park Quang Trung Software City Danang Hi-tech Park === Europe === Austria Softwarepark Hagenberg: Hagenberg, Upper Austria VRVis Research Center: Vienna Belarus Belarus High Technologies Park: Minsk Belgium BioWin: The Health Cluster of Wallonia Bulgaria Sofia Tech Park: Sofia Czech Republic South Moravian Innovation Centre (Czech: Jihomoravské inovační centrum, JIC) is a Czech association of legal entities in Brno, Czech Republic that supports companies and connects them with universities and research institutions. Vědeckotechnický park (Plzeň) Finland Otaniemi: near Helsinki


id: list-of-technology-centers-20260505-3
file: data/en.wikipedia.org/wiki/List_of_technology_centers-3.md
category: reference
title: List of technology centers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_technology_centers
date_saved: 2026-05-05T08:20:15.012774+00:00
instance: kb-cron
parent: list-of-technology-centers-20260505-0
summary:
==== United States ==== Philicon Valley (also known as "Silicon Valley Forge"): Area close to Philadelphia, in the suburbs of Valley Forge and Wayne Silicon Alley: Originally a portion of Manhattan in New York City, specifically Broadway, the Flatiron District, SoHo, and TriBeCa. Now encompasses the general NYC tech sphere. Silicon Anchor: Norfolk–Virginia Beach metropolitan area Silicon Basin: Columbus, Ohio Silicon Bayou: New Orleans, Louisiana Silicon Beach: Santa Monica, California and the Westside area of the Los Angeles metro, more specifically Culver City, Venice Beach, Westwood, Manhattan Beach, Malibu, Playa del Rey, and Marina del Rey; also used to refer to the San Diego area in the name of the 1980s software developer Silicon Beach Software. There is also Silicon Beach in South Florida in the Miami area. Silicon Coast: Orange County, California Silicon Desert: Chandler, Arizona Silicon Forest: Portland, Oregon Silicon Harbor: Charleston, South Carolina Silicon Hill: Washington, D.C. Silicon Hills: Austin, Texas Silicon Hollar: Boone, North Carolina Silicon Mountain: Front Range Urban Corridor, Colorado (Denver, Boulder, Fort Collins, Colorado Springs) Silicon Peach: Atlanta home to Georgia Institute of Technology as well as VMware Airwatch, Google ATL, Kabbage, Pindrop Security, and many venture capital firms Silicon Prairie Dallas-Fort Worth


id: list-of-science-centers-in-the-united-states-20260505-0
file: data/en.wikipedia.org/wiki/List_of_science_centers_in_the_United_States-0.md
category: reference
title: List of science centers in the United States
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_science_centers_in_the_United_States
date_saved: 2026-05-05T08:20:16.362844+00:00
instance: kb-cron
parent: list-of-science-centers-in-the-united-states-20260505-0
summary:
This is a list of science centers in the United States. American Alliance of Museums (AAM) and Association of Science and Technology Centers (ASTC) member centers are granted institutional benefits and may offer benefits to individuals through purchased or granted individual memberships as well. ASTC offers a "passport" that allows for free general entry at all other participating ASTC member centers outside of a 90-mile radius of home. AAM offers a similar program that offers benefits to individuals. AAM accredited museums have obtained a seal of approval from the AAM Accreditation Program that ensures a museum's "commitment to excellence, accountability, high professional standards and continued institutional improvement." == See also == List of museums in the United States List of natural history museums in the United States List of science museums List of university museums in the United States == References ==


id: list-of-volunteer-computing-projects-20260505-0
file: data/en.wikipedia.org/wiki/List_of_volunteer_computing_projects-0.md
category: reference
title: List of volunteer computing projects
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_volunteer_computing_projects
date_saved: 2026-05-05T08:20:17.820222+00:00
instance: kb-cron
parent: list-of-volunteer-computing-projects-20260505-0
summary:
Volunteer computing projects are a type of distributed computing where volunteers donate computing time to specific causes. The donated computing power comes from idle CPUs and GPUs in personal computers, video game consoles, and Android devices. Each project seeks to utilize the computing power of many internet connected devices to solve problems and perform large scale computational research in a cost-effective manner. == Active projects == == Completed projects == == See also == == References ==


id: list-of-vertebrate-fauna-of-the-campanian-stage-20260505-0
file: data/en.wikipedia.org/wiki/List_of_vertebrate_fauna_of_the_Campanian_stage-0.md
category: reference
title: List of vertebrate fauna of the Campanian stage
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_vertebrate_fauna_of_the_Campanian_stage
date_saved: 2026-05-05T08:20:20.913864+00:00
instance: kb-cron
parent: list-of-vertebrate-fauna-of-the-campanian-stage-20260505-0
summary:
This is an incomplete list that briefly describes vertebrates that were extant during the Campanian, a stage of the Late Cretaceous Period which extended from 83.6 to 72.1 million years before present. Animals that lived in the Campanian include: == Cartilaginous fish == === Chimaeriformes === === †Hybodontiformes === === Selachimorpha === === Batoidea === == Actinopterygii == === Chondrostei === === Holostei === === Teleosteomorpha === == Actinistia == == Dipnoi == == Amphibians == == Lepidosaurs == == Testudines == == †Plesiosaurs == == †Choristoderans == == Crocodylomorphs == == †Pterosaurs == == Dinosaurs == During the Campanian age, a radiation among dinosaur species occurred. In North America, for example, the number of known dinosaur genera rises from 4 at the base of the Campanian to 48 in the upper part. This development is sometimes referred to as the "Campanian Explosion". However, it is not yet clear if the event is artificial, i.e. the low number of genera in the lower Campanian can be caused by a lower preservation chance for fossils in deposits of that age. The generally warm climates and large continental area covered in shallow sea during the Campanian probably favoured the dinosaurs. In the


id: list-of-vertebrate-fauna-of-the-maastrichtian-stage-20260505-0
file: data/en.wikipedia.org/wiki/List_of_vertebrate_fauna_of_the_Maastrichtian_stage-0.md
category: reference
title: List of vertebrate fauna of the Maastrichtian stage
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_vertebrate_fauna_of_the_Maastrichtian_stage
date_saved: 2026-05-05T08:20:22.223337+00:00
instance: kb-cron
parent: list-of-vertebrate-fauna-of-the-maastrichtian-stage-20260505-0
summary:
This is an incomplete list that briefly describes vertebrates that were extant during the Maastrichtian, a stage of the Late Cretaceous Period which extended from 72.1 to 66 million years before present. This was the last time period in which non-avian dinosaurs, pterosaurs, plesiosaurs, and mosasaurs existed. == Amphibians == == Dinosaurs == === †Ornithischians === ==== †Ankylosaurs ==== ==== †Parksosauridae ==== ==== †Ornithopoda ==== ==== †Ceratopsians ==== ==== †Pachycephalosaurs ==== === †Sauropods === === †Theropods (non-maniraptoran) === ==== †Maniraptora (non-avian) ==== ===== Avialans (avian theropods) ===== == Cartilaginous fish == == Crocodylomorphs == == Ray-finned fish == == Mammals == == †Plesiosaurs == == †Pterosaurs == == Squamates == == Turtles == == †Choristoderes == == References == == See also == List of fossil sites (with link directory) Cretaceous–Paleogene extinction event List of vertebrate fauna of the Campanian stage


id: list-of-extinct-rodents-20260505-0
file: data/en.wikipedia.org/wiki/List_of_extinct_rodents-0.md
category: reference
title: List of extinct rodents
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_extinct_rodents
date_saved: 2026-05-05T08:20:23.473516+00:00
instance: kb-cron
parent: list-of-extinct-rodents-20260505-0
summary:
This list is of rodent species that are extinct − no longer alive. Species from related groups such as Lagomorpha (rabbits and hares) are not included. == Before 1500 == == Extinct after 1500 == === 16th century === Oriente cave rat Torre's cave rat Imposter hutia Montane hutia Megaoryzomys Cuban coney Hispaniolan edible rat Conilurus capricornensis Samaná hutia Buhler's coryphomys Noronhomys Pennatomys nivalis Desmarest's hutia === 17th century === Insular cave rat Puerto Rican hutia Verhoeven's giant tree rat == See also == Extinct rodents – all periods Prehistoric rodents Rodent extinctions since 1500 == References ==


id: timeline-of-extinctions-in-the-holocene-20260505-0
file: data/en.wikipedia.org/wiki/Timeline_of_extinctions_in_the_Holocene-0.md
category: reference
title: Timeline of extinctions in the Holocene
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Timeline_of_extinctions_in_the_Holocene
date_saved: 2026-05-05T08:20:25.482172+00:00
instance: kb-cron
parent: timeline-of-extinctions-in-the-holocene-20260505-0
summary:
This article is a list of biological species, subspecies, and evolutionary significant units that are known to have become extinct during the Holocene, the current geologic epoch, ordered by their known or approximate date of disappearance from oldest to most recent. The Holocene is considered to have started with the Holocene glacial retreat around 11650 years Before Present (c. 9700 BC). It is characterized by a general trend towards global warming, the expansion of anatomically modern humans (Homo sapiens) to all emerged land masses, the appearance of agriculture and animal husbandry, and a reduction in global biodiversity. The latter, dubbed the sixth mass extinction in Earth history, is largely attributed to increased human population and activity, and may have started already during the preceding Pleistocene epoch with the demise of the Pleistocene megafauna. The following list is incomplete by necessity, since the majority of extinctions are thought to be undocumented, and for many others there isn't a definitive, widely accepted last, or most recent record. According to the species-area theory, the present rate of extinction may be up to 140,000 species per year. == 10th millennium BC == == 9th millennium BC == == 8th millennium BC == == 7th


id: lists-of-prehistoric-fish-20260505-0
file: data/en.wikipedia.org/wiki/Lists_of_prehistoric_fish-0.md
category: reference
title: Lists of prehistoric fish
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lists_of_prehistoric_fish
date_saved: 2026-05-05T08:20:26.884768+00:00
instance: kb-cron
parent: lists-of-prehistoric-fish-20260505-0
summary:
Prehistoric fish are early fish that are known only from fossil records. They are the earliest known vertebrates, and include the first and extinct fish that lived through the Cambrian to the Quaternary. The study of prehistoric fish is called paleoichthyology. A few living forms, such as the coelacanth are also referred to as prehistoric fish, or even living fossils, due to their current rarity and similarity to extinct forms. Fish which have become recently extinct are not usually referred to as prehistoric fish. Lists of various prehistoric fishes include: List of prehistoric jawless fish List of placoderms List of acanthodians List of prehistoric cartilaginous fish List of prehistoric bony fish List of indeterminate prehistoric percomorph genera List of sarcopterygians == See also == Evolution of fish Prehistoric life Vertebrate paleontology == References == == Further reading == Janvier, Philippe (1998) Early Vertebrates, Oxford, New York: Oxford University Press. ISBN 0-19-854047-7 Long, John A. (1996) The Rise of Fishes: 500 Million Years of Evolution, Baltimore: The Johns Hopkins University Press. ISBN 0-8018-5438-5 == External links == Fossil Fish


id: list-of-fossil-parks-20260505-0
file: data/en.wikipedia.org/wiki/List_of_fossil_parks-0.md
category: reference
title: List of fossil parks
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_fossil_parks
date_saved: 2026-05-05T08:20:31.281395+00:00
instance: kb-cron
parent: list-of-fossil-parks-20260505-0
summary:
Following is a list of protected areas where fossils are preserved, known as fossil parks or fossil reserves, worldwide by country. == Africa == === Egypt === Wadi Al-Hitan - Valley of The Whales, Fayyoum, Western Desert === South Africa === West Coast Fossil Park, Langebaanweg, Western Cape === Tanzania === == Asia == === India === There are two geological parks maintained by the Geological Survey of India: Dinosaur Fossils National Park, Dhar, Madhya Pradesh Shivalik Fossil Park, Saketi, H.P. Salkhan Fossils Park, Sonbhadra, U.P. Mandla Plant Fossils National Park Indroda Dinosaur and Fossil Park, Gandhinagar, Gujarat National Fossil Wood Park, Tiruvakkarai National Fossil Wood Park, Sathanur Akal Wood Fossil Park, Jaisalmer, Rajasthan Amkhoi Fossil Park, West Bengal. === Japan === Sendai City Tomizawa Site Museum houses a fossilized forest and human artifacts === Thailand === == Australia == === Australia === ==== Victoria ==== Dinosaur Dreaming Dinosaur Cove ==== Queensland ==== Riversleigh ==== South Australia ==== Lake Callabonna Fossil Reserve Lake Ngapakaldi to Lake Palankarinna Fossil Area Maslin Bay - Aldinga Bay Geological Site Naracoorte Caves National Park Nilpena Ediacara National Park Willalinchina Sandstone Fossil Flora site, near Woomera == North America == === Canada === Ancient Echoes


id: list-of-fossil-sites-20260505-0
file: data/en.wikipedia.org/wiki/List_of_fossil_sites-0.md
category: reference
title: List of fossil sites
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_fossil_sites
date_saved: 2026-05-05T08:20:32.506792+00:00
instance: kb-cron
parent: list-of-fossil-sites-20260505-0
summary:
This list of fossil sites is a worldwide list of localities known well for the presence of fossils. Some entries in this list are notable for a single, unique find, while others are notable for the large number of fossils found there. Many of the entries in this list are considered Lagerstätten (sedimentary deposits that exhibits extraordinary fossils with exceptional preservation—sometimes including preserved soft tissues). Lagerstätten are indicated by a note () in the noteworthiness column. Fossils may be found either associated with a geological formation or at a single geographic site. Geological formations consist of rock that was deposited during a specific period of time. They usually extend for large areas, and sometimes there are different important sites in which the same formation is exposed. Such sites may have separate entries if they are considered to be more notable than the formation as a whole. In contrast, extensive formations associated with large areas may be equivalently represented at many locations. Such formations may be listed either without a site, with a site or sites that represent the type locality, or with multiple sites of note. When a type locality is listed as the site for a formation with many


id: lists-of-fossiliferous-stratigraphic-units-20260505-0
file: data/en.wikipedia.org/wiki/Lists_of_fossiliferous_stratigraphic_units-0.md
category: reference
title: Lists of fossiliferous stratigraphic units
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lists_of_fossiliferous_stratigraphic_units
date_saved: 2026-05-05T08:20:33.899571+00:00
instance: kb-cron
parent: lists-of-fossiliferous-stratigraphic-units-20260505-0
summary:
== By location == Lists of fossiliferous stratigraphic units in Africa List of fossiliferous stratigraphic units in Antarctica Lists of fossiliferous stratigraphic units in Asia List of fossiliferous stratigraphic units in the Caribbean Lists of fossiliferous stratigraphic units in Europe Lists of fossiliferous stratigraphic units in North America Lists of fossiliferous stratigraphic units in Canada Lists of fossiliferous stratigraphic units in the United States Lists of fossiliferous stratigraphic units in Oceania Lists of fossiliferous stratigraphic units in South America == By preserved taxon == List of dinosaur-bearing stratigraphic units List of phytosaur-bearing stratigraphic units List of plesiosaur-bearing stratigraphic units List of pterosaur-bearing stratigraphic units List of thalattosuchian-bearing stratigraphic units == See also == List of fossil sites Paleontology lists Paleontological sites Stratigraphy


id: list-of-lagerst-tten-20260505-0
file: data/en.wikipedia.org/wiki/List_of_lagerstätten-0.md
category: reference
title: List of lagerstätten
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_lagerstätten
date_saved: 2026-05-05T08:20:36.097809+00:00
instance: kb-cron
parent: list-of-lagerst-tten-20260505-0
summary:
The list of Lagerstätten is a documentation of Lagerstätte fossils sites around the world, arranged by geologic age. These are characterized by exceptional preservation of fossil organisms, regularly including many well-preserved animals and their soft tissue remains. The extent of Lagerstätten deposits can range from a select site or stratigraphic layer to a whole formation or group. Some sites that one author calls a single Lagerstätte may be called multiple by another (such as the Jehol Biota and the Yixian/Jiufotang Formations). This list attempts to note this in the text and provide the formation or stratigraphic unit from which a site came. == Criteria == Sites on the list must either: Be referred to as a Lagerstätte within the main text of at least one scientific publication. Similar terms, such as 'exceptional preservation', do not qualify. Have fossils that fulfill the criteria of Konservat-Lagerstätte as set within Kimmig & Julien (2024): Konservat-Lagerstätten are characterized by exceptional preservation, and at least 5% of the fossils recovered from a site must preserve either soft tissue remains or nearly complete individuals, preferably both. == List == === Precambrian === === Cambrian === === Ordovician === === Silurian === === Devonian === === Carboniferous


id: list-of-non-dinosauria-fossil-trackway-articles-20260505-0
file: data/en.wikipedia.org/wiki/List_of_non-Dinosauria_fossil_trackway_articles-0.md
category: reference
title: List of non-Dinosauria fossil trackway articles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_non-Dinosauria_fossil_trackway_articles
date_saved: 2026-05-05T08:20:37.267674+00:00
instance: kb-cron
parent: list-of-non-dinosauria-fossil-trackway-articles-20260505-0
summary:
This is a list of articles relating to fossil trackways that are outside the category of the numerous fossil dinosaur articles – that refer to tracks or trackways. == List of non-Dinosauria fossil trackway articles == Archaeotherium Arthropleura Chirotherium; (only a related species known) Climactichnites Cruziana Dromornithidae Eurypterid Hibbertopterus Laetoli Laetoli footprints Pterosaur Tetrapod Trace fossil Trilobite === Location, site articles === Chuckanut Formation Coconino Sandstone Ipolytarnóc Minas Basin; "fish-fin" trackway Valentia Island == See also == Protichnites Trace fossil


id: list-of-paleotempestology-records-20260505-0
file: data/en.wikipedia.org/wiki/List_of_paleotempestology_records-0.md
category: reference
title: List of paleotempestology records
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_paleotempestology_records
date_saved: 2026-05-05T08:20:38.755428+00:00
instance: kb-cron
parent: list-of-paleotempestology-records-20260505-0
summary:
Paleotempestology is the study of past tropical cyclone activity by means of geological proxies as well as historical documentary records. The term was coined by American meteorologist Kerry Emanuel. == Examples == === Non-tropical examples === == See also == Tropical cyclone Tropical cyclone observation Tropical cyclones and climate change == Notes == == References == === Citations === === General sources === == Further reading == Elsner, James B.; Kara, A. Birol (1999). Hurricanes of the North Atlantic: Climate and Society. New York: Oxford University Press. pp. 49–51, 378. ISBN 978-0-19-512508-5. Huang, Yun (2009-01-01). "Sediment records of modern and prehistoric hurricane strikes in Weeks Bay, Alabama". LSU Master's Theses. doi:10.31390/gradschool_theses.1922. S2CID 135330841. Kar, Devyani (2010-01-01). "Integration of paleotempestology with coastal risk and vulnerability assessment: case studies from the Dominican Republic and Nicaragua". LSU Doctoral Dissertations. doi:10.31390/gradschool_dissertations.2009. S2CID 134409924. Knowles, Jason (2004-01-01). "Coastal lake-sediment records of prehistoric hurricane strikes in Honduras and Turks and Caicos Islands of the Caribbean basin". LSU Master's Theses. doi:10.31390/gradschool_theses.3433. S2CID 134921929. Liu, Kam-biu (2004). "Paleotempestology: Principles, Methods, and Examples from Gulf Coast Lake Sediments". In Murnane, R. J.; Liu, Kam-biu (eds.). Hurricanes and Typhoons: Past, Present, and Future. New York: Columbia University Press. pp. 13–57.


id: list-of-lost-fossil-sites-20260505-0
file: data/en.wikipedia.org/wiki/List_of_lost_fossil_sites-0.md
category: reference
title: List of lost fossil sites
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_lost_fossil_sites
date_saved: 2026-05-05T08:20:39.936510+00:00
instance: kb-cron
parent: list-of-lost-fossil-sites-20260505-0
summary:
This list of lost fossil sites is a list of localities in which abundant, well-preserved, or scientifically significant fossils were once found but are no longer available due to the destruction, inaccessibility or overcollection of the fossils preserved therein. == The list == == See also == List of lost, damaged, or destroyed dinosaur specimens


id: paleobiota-of-the-ca-ad-n-asfalto-formation-20260505-0
file: data/en.wikipedia.org/wiki/Paleobiota_of_the_Cañadón_Asfalto_Formation-0.md
category: reference
title: Paleobiota of the Cañadón Asfalto Formation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paleobiota_of_the_Cañadón_Asfalto_Formation
date_saved: 2026-05-05T08:20:41.216146+00:00
instance: kb-cron
parent: paleobiota-of-the-ca-ad-n-asfalto-formation-20260505-0
summary:
The Cañadón Asfalto Formation is a geological formation which dates to the Toarcian age of the Early Jurassic period of Argentina. The rocks of the formation preserve a diverse biota, including plants, dinosaurs, invertebrates, mammals and pterosaurs, among others. The formation is divided into two members: the lower Las Chacritas Member, and the overlying Puesto Almada member, though the latter has also been assigned to the overlying Cañadón Calcáreo Formation by some authors. The members are typically composed of fluvial-lacustrine deposits consisting of sandstones and shales, with a limestone carbonate evaporitic sequence also being present in the lower of the two. == Invertebrates == === Demospongiae === === Crustacea === === Mollusca === === Insecta === Insect eggs of unknown affinity were reported from several layers of the Estancia Fossati locality. == Vertebrates == === Fish === === Amphibians === === Turtles === === Lepidosaurs === === Crocodylomorpha === === Pterosaurs === === Dinosaurs === ==== Theropods ==== During a campaign conducted in early 2021, remains of a large theropod dinosaur were found near the town of Las Chacritas. In 2020 a new fossil locality was found, named Cañadón de las Huellas, due to the large number of sauropods, and


id: paleobiota-of-the-djadochta-formation-20260505-0
file: data/en.wikipedia.org/wiki/Paleobiota_of_the_Djadochta_Formation-0.md
category: reference
title: Paleobiota of the Djadochta Formation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paleobiota_of_the_Djadochta_Formation
date_saved: 2026-05-05T08:20:42.425794+00:00
instance: kb-cron
parent: paleobiota-of-the-djadochta-formation-20260505-0
summary:
The Djadochta Formation (sometimes spelled Djadokhta, Djadokata, or Dzhadokhtskaya) is a geological formation in the Gobi Desert of Mongolia. It dates to the Campanian stage of the Late Cretaceous and is famous for its dinosaur fossils including Oviraptor, Protoceratops, and Velociraptor. It is also known for a high diversity of mammal and lizard fossils, and a complete catalogue of its fossil contents is shown below. == Vertebrates == === Amphibians === === Crocodylomorphs === === Lizards === === Mammals === ==== Multituberculates ==== ==== Therians ==== === Pterosaurs === === Turtles === === Dinosaurs === ==== Ankylosaurids ==== ==== Marginocephalians ==== ==== Ornithopods ==== ==== Sauropods ==== ==== Theropods ==== ===== Alvarezsaurs ===== ===== Birds ===== ===== Dromaeosaurs ===== ===== Non-maniraptoran theropods ===== ===== Oviraptorosaurs ===== ===== Troodontids ===== == Flora == == See also == Fighting Dinosaurs Flaming Cliffs List of Asian dinosaurs List of pterosaur-bearing stratigraphic units List of stratigraphic units with dinosaur body fossils Paleobiota of the Yixian Formation Roy Chapman Andrews == References ==


id: paleobiota-of-the-hell-creek-formation-20260505-0
file: data/en.wikipedia.org/wiki/Paleobiota_of_the_Hell_Creek_Formation-0.md
category: reference
title: Paleobiota of the Hell Creek Formation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paleobiota_of_the_Hell_Creek_Formation
date_saved: 2026-05-05T08:20:44.233790+00:00
instance: kb-cron
parent: paleobiota-of-the-hell-creek-formation-20260505-0
summary:
This is an overview of the fossil flora and fauna of the Maastrichtian-Danian Hell Creek Formation. == Invertebrates == === Insects === Insects from the groups Diptera, Zygoptera, and possibly Hemiphlebiidae have been unearthed in Hell Creek in amber. Fossils found in the Hell Creek Formation and the Fort Union Formation of these insects went extinct during the K-T Event. === Molluscs === == Amphibians == == Fish == === Bony fish === === Cartilaginous fish === == Dinosaurs == A paleo-population study is one of the most difficult of analyses to conduct in field paleontology. Here is the most recent estimate of the proportions of the eight most common dinosaurian families in the Hell Creek Formation, based on detailed field studies by White, Fastovsky and Sheehan. Ceratopsidae 61% Hadrosauridae 23% Ornithomimidae 5% Tyrannosauridae 4% Hypsilophodontidae 3% Dromaeosauridae 2% Pachycephalosauridae 1% Ankylosauridae 1% Troodontidae 1% (represented only by teeth) Outcrops sampled by the Hell Creek Project were divided into three sections: lower, middle and upper slices. The top and bottom sections were the focus of the PLoS One report, and within each portion many remains of Triceratops, Edmontosaurus, and Tyrannosaurus were found. Triceratops was the most common in each section,


id: paleobiota-of-the-hell-creek-formation-20260505-1
file: data/en.wikipedia.org/wiki/Paleobiota_of_the_Hell_Creek_Formation-1.md
category: reference
title: Paleobiota of the Hell Creek Formation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paleobiota_of_the_Hell_Creek_Formation
date_saved: 2026-05-05T08:20:44.233790+00:00
instance: kb-cron
parent: paleobiota-of-the-hell-creek-formation-20260505-0
summary:
==== Eumaniraptorans ==== Historically, numerous teeth have been attributed to various dromaeosaurid and troodontid taxa with known body fossils from only older formations, including Saurornithoides, Zapsalis, Dromaeosaurus, Saurornitholestes, and Troodon. However, in a 2013 study, Evans et al. concluded that there is little evidence for more than a single dromaeosaurid taxon, Acheroraptor, in the Hell Creek-Lance assemblages, which would render these taxa invalid for this formation. This was seemingly disproven in 2015, when DePalma et al., described the new genus Dakotaraptor, a large species of dromaeosaur. However, Dakotaraptor's validity has been called into question since, as the holotype may be a chimeric assemblage of various non-dromaeosaurid coelurosaurians. Fossilized teeth of various troodontids and coelurosaurs are common throughout the Hell Creek Formation; the best known examples include Paronychodon, Pectinodon and Richardoestesia, respectively. Teeth belonging to possible intermediate species of Dromaeosaurus and Saurornitholestes have been unearthed at the Hell Creek Formation and the nearby Lance Formation. == Pterosaurs == Undescribed pterosaur remains were reported from North Dakota. Undescribed pteranodontian specimen has also been mentioned in the supplementary material of Longrich et al. (2018). == Crocodylomorphs == == Turtles == == Squamata == == Choristoderans == == Mammals == === Multituberculates === ===


id: paleobiota-of-the-hell-creek-formation-20260505-2
file: data/en.wikipedia.org/wiki/Paleobiota_of_the_Hell_Creek_Formation-2.md
category: reference
title: Paleobiota of the Hell Creek Formation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paleobiota_of_the_Hell_Creek_Formation
date_saved: 2026-05-05T08:20:44.233790+00:00
instance: kb-cron
parent: paleobiota-of-the-hell-creek-formation-20260505-0
summary:
There is evidence of transitional floras in the middle of the Hell Creek Formation as shown by HCII and HCIII zones. The HCII flora represents a transitional period where taxa from the lower Hell Creek are replaced by the HCIII flora. The diversity of the HCIII zone is very high, and its composition is more uniform than that of HCII, many of which were rare or absent from the zones below, and some others that used to be common below became rarer in the HCIII zone. These forms include Elatides longifolia, "Dryophyllum" tennessensis, Liriodendrites bradacii, and many members of the Laurales including Bisonia niemii, "Ficus" planicostata, and Marmarthia trivialis, while "Celastrus" taurenensis, Leepierceia preartocarpoides, and many cupressaceous conifers became rarer. This phenomenon suggests that the global temperature was warming during the last 300,000-500,000 years of the Cretaceous period. There is no evidence of fern prairie in the Hell Creek Formation. However, there was high angiosperm diversity — common plane trees, "Dryophyllum" subfalcatum, Leepierceia preartocarpoides, and sabal palms — along with extinct cycadeoid Nilssoniocladus, Ginkgo, araucariaceous, Taxodiaceous, and cupressaceous conifers. This represents the mixed deciduous and evergreen broad-leaved forest of the Hell Creek landscape. The nature of these forests is uncertain


id: paleobiota-of-the-hell-creek-formation-20260505-3
file: data/en.wikipedia.org/wiki/Paleobiota_of_the_Hell_Creek_Formation-3.md
category: reference
title: Paleobiota of the Hell Creek Formation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paleobiota_of_the_Hell_Creek_Formation
date_saved: 2026-05-05T08:20:44.233790+00:00
instance: kb-cron
parent: paleobiota-of-the-hell-creek-formation-20260505-0
summary:
=== Bibliography === General Broad, William J.; Chang, Kenneth (29 March 2019), "Fossil Site Reveals Day That Meteor Hit Earth and, Maybe, Wiped Out Dinosaurs", The New York Times Preston, Douglas (2019), "The Day the Dinosaurs Died", The New Yorker, p. 1, retrieved 2019-04-01 U.S. National, Park Service (1966), National Natural Landmarks - National Natural Landmarks (U.S. National Park Service), www.nps.gov, p. 1, retrieved 2019-03-22 Geology DePalma, Robert A.; Smit, Jan; Burnham, David A.; Kuiper, Klaudia; Manning, Phillip L.; Oleinik, Anton; Larson, Peter; Maurrasse, Florentin J.; Vellekoop, Johan; Richards, Mark A.; Gurche, Loren; Alvarez, Walter (2019), "A seismically induced onshore surge deposit at the K-Pg boundary, North Dakota", Proceedings of the National Academy of Sciences, 116 (17): 8190–8199, Bibcode:2019PNAS..116.8190D, doi:10.1073/pnas.1817407116, PMC 6486721, PMID 30936306 Bibcode:2019PNAS..116.8190D Evans, D.C.; Larson, D.W.; Currie, P.J. (2013), "A new dromaeosaurid (Dinosauria: Theropoda) with Asian affinities from the latest Cretaceous of North America", Naturwissenschaften, 100 (11): 1041–1049, Bibcode:2013NW....100.1041E, doi:10.1007/s00114-013-1107-5, PMID 24248432 Bibcode:2013NW....100.1041E Husson, D.; Galbrun, B.; Laskar, J.; Hinnov, L.A.; Thibault, N.; Gardin, S.; Locklair, R.E. (2011), "Astronomical calibration of the Maastrichtian (late Cretaceous)", Earth and Planetary Science Letters, 305 (3): 328–340, Bibcode:2011E&PSL.305..328H, doi:10.1016/j.epsl.2011.03.008 Bibcode:2011E&PSL.305..328H LeCain, Rebecca (2010), "Magnetostratigraphy of the Hell Creek and lower Fort


id: paleobiota-of-the-yixian-formation-20260505-0
file: data/en.wikipedia.org/wiki/Paleobiota_of_the_Yixian_Formation-0.md
category: reference
title: Paleobiota of the Yixian Formation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paleobiota_of_the_Yixian_Formation
date_saved: 2026-05-05T08:20:45.785312+00:00
instance: kb-cron
parent: paleobiota-of-the-yixian-formation-20260505-0
summary:
The Yixian Formation (simplified Chinese: 义县组; traditional Chinese: 義縣組; pinyin: Yìxiàn zǔ) is a geological formation in Jinzhou, Liaoning, People's Republic of China, that spans about 1.6 million years during the early Cretaceous period (Barremian-Aptian stage). It is known for its fossils, listed below. The Yixian Formation is divided into the following subunits: (ages from Zhong et al., 2021 unless otherwise noted) Upper Yixian (124.1 Ma) ("Jingangshan Bed") ("Dawangzhangzi Bed") Upper Lava Unit Jianshangou Unit (125.46 Ma) Lower Lava Unit Lujiatun Unit (125.76–125.68 Ma) == Sauropods == == Ornithischians == The dinosaurs listed below were compiled in a survey by Xu and Norell in 2006, unless otherwise noted. === Ankylosaurs === === Ceratopsians === === Ornithopods === == Theropods == The dinosaurs listed below were compiled in a survey by Xu and Norell in 2006, unless otherwise noted. === Avialans === === Compsognathids === === Dromaeosaurs === === Ornithomimosaurs === === Oviraptorosaurs === === Therizinosaurs === === Troodontids === === Tyrannosaurs and other theropods === == Pterosaurs == The pterosaurs listed below were compiled in a survey by Wang and Zhou in 2006, unless otherwise noted. == Misc. reptiles == === Choristoderans === === Lizards === === Turtles === ==


id: list-of-paleontologists-20260505-0
file: data/en.wikipedia.org/wiki/List_of_paleontologists-0.md
category: reference
title: List of paleontologists
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_paleontologists
date_saved: 2026-05-05T08:20:46.992705+00:00
instance: kb-cron
parent: list-of-paleontologists-20260505-0
summary:
This is a list of notable paleontologists who have made significant contributions to the field of paleontology. Only paleontologists with biographical articles in Wikipedia are listed here. == A == == B == == C == == D == == E == == F == == G == == H == == I == Nizar Ibrahim (Germany / Morocco, 1982- ) Thomas Image (England, 1772-1856) Wataru Ishijima (Japan, 1906-1980) Arturo Issel (Italy, 1842-1922) == J == David Jablonski (United States, 1953- ) Auguste Jaccard (Switzerland, 1833-1895) Louis L. Jacobs (United States, 1948- ) Sohan Lal Jain (India) Helen F. James (United States, 1956- ) Werner Janensch (Germany, 1878-1969) Philippe Janvier (France) Erik Jarvik (Sweden, 1829-1901) Dick Jefferies (England) Farish Jenkins (United States, 1940-2012) James A. Jensen (United States, 1918-1998) Kirk Johnson (United States, 1960- ) Frederik Johnstrup (Denmark, 1818-1894) Theobald Jones (Ireland, 1790-1868) Thomas Rupert Jones (England, 1819-1911) == K == == L == == M == == N == Darren Naish (England, 1975- ) Alfred Gabriel Nathorst (Sweden, 1850-1921) Theodor Anton Neagu (Romania, 1932-2017) Sterling Nesbitt (United States, 1982- ) Edwin Tulley Newton (England, 1840-1930) Elizabeth Nicholls (Canada, 1946-2004) Henry Alleyne Nicholson (Scotland, 1844-1899) Adolf Carl Noé (Austria /


id: list-of-small-shelly-fossil-taxa-20260505-0
file: data/en.wikipedia.org/wiki/List_of_small_shelly_fossil_taxa-0.md
category: reference
title: List of small shelly fossil taxa
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_small_shelly_fossil_taxa
date_saved: 2026-05-05T08:20:48.210973+00:00
instance: kb-cron
parent: list-of-small-shelly-fossil-taxa-20260505-0
summary:
This is a list of small shelly fossils of prehistoric marine animals, ordered by their type. == Whole-organism == Namacalathus == Monoplacophoran-like == Yochelsoniella == Scleritome elements == Elements of a scleritome, resembling Halkieria: Halkieria Probable palaeoscolecid worm sclerites: Palaeoscolex Maikhanella Tomotiid-like sclerites: Micrina Eccentrotheca == Conical == Problematic cones: Cyrtochites Paradoxiconus Probable Lobopodian sclerites: Rhombocorniculum Rushtonites Mongolitubulus == Net-like == Microdictyon Onychodictyon Quadrataporata == Sponge spicule-like == Chancelloria == Tubular == Sinotubulites Anabarites Hyolithellus Torellella == See also == Prehistoric marine animals Fossil record of animals Paleontology lists == References == === Inline citations === === Resources referenced === A further list available in Li, G.; Steiner, M.; Zhu, X.; Yang, A.; Wang, H.; Erdtmann, B. D. (2007). "Early Cambrian metazoan fossil record of South China: Generic diversity and radiation patterns". Palaeogeography, Palaeoclimatology, Palaeoecology. 254 (1–2): 229–249. doi:10.1016/j.palaeo.2007.03.017. More in Steiner, M.; Li, G.; Qian, Y.; Zhu, M. (2004). "Lower Cambrian Small Shelly Fossils of northern Sichuan and southern Shaanxi (China), and their biostratigraphic importance". Geobios. 37 (2): 259. doi:10.1016/j.geobios.2003.08.001.


id: list-of-commonly-used-taxonomic-affixes-20260505-0
file: data/en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes-0.md
category: reference
title: List of commonly used taxonomic affixes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes
date_saved: 2026-05-05T08:20:49.524905+00:00
instance: kb-cron
parent: list-of-commonly-used-taxonomic-affixes-20260505-0
summary:
This is a list of common affixes used when scientifically naming species, particularly extinct species for whom only their scientific names are used, along with their derivations.


id: list-of-commonly-used-taxonomic-affixes-20260505-1
file: data/en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes-1.md
category: reference
title: List of commonly used taxonomic affixes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes
date_saved: 2026-05-05T08:20:49.524905+00:00
instance: kb-cron
parent: list-of-commonly-used-taxonomic-affixes-20260505-0
summary:
a-, an-: Pronunciation: /ə/, /a/, /ən/, /an /. Origin: Ancient Greek: ἀ-, ἀν- (a, an-). Meaning: a prefix used to make words with a sense opposite to that of the root word; in this case, meaning 'without' or '-less'. This is usually used to describe organisms without a certain typical characteristic, as well as organisms in which that characteristic may not be immediately obvious. Examples: Anurognathus ('tailless jaw'); Apus ('footless'); Apteryx ('wingless'); Pteranodon ('wings without teeth'); Anura ('tailless'); Anophthalmus ('eyeless'); Aceros ('hornless'); Agnatha ('jawless'); Aceratherium ('hornless beast'); Arrhinoceratops ('noseless horned face'); Apterodon ('teeth without wings') -acanth, acantho-: Pronunciation: /eɪkænθ/, /eɪkænθoʊ/. Origin: Ancient Greek: ἄκανθα (ákantha). Meaning: spine, thorn. Examples: Acanthodes ('spiny base'); Acanthostega ('spine roof'); coelacanth ('hollow spine'); Acrocanthosaurus ('high-spined lizard'); Acanthoderes ('spiny neck'); Acanthamoeba ('spiny amoeba'); Metriacanthosaurus ('moderately-spined lizard'); Holacanthus ('full spine'); Triacanthus ('three spine'); Acanthaster ('spine star'); Acanthocephala ('spine head'), Anisacanthus ('unequal spine'); Acanthoceras ('spine horn'): Acanthogeophilus ('spiny earth-lover'); Acanthosicyos ('spiny gourd'); Acanthophis ('spiny snake'); Acanthomyrmex ('spiny ant') aeto-: Pronunciation: /aɛto/. Origin: Ancient Greek: ἀετός (aetós). Meaning: eagle. Examples: Aetonyx ('eagle claw'); Aetobatus ('eagle ray'); Aetosauria ('eagle lizard'); Ichthyaetus ('fish eagle') afro-: Pronunciation: /ˈafro/. Origin: Latin: afro-. Meaning: African. Examples: Afrovenator (African hunter); Afropithecus (African ape); Afrotheria (African


id: list-of-commonly-used-taxonomic-affixes-20260505-2
file: data/en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes-2.md
category: reference
title: List of commonly used taxonomic affixes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes
date_saved: 2026-05-05T08:20:49.524905+00:00
instance: kb-cron
parent: list-of-commonly-used-taxonomic-affixes-20260505-0
summary:
Examples: Artiodactyla ('even toe'); Pterodactylus ('wing finger'); Perissodactyla ('uneven toe'); Ctenodactylus ('comb finger'); Phyllodactylus ('leaf finger'); Hemiphyllodactylus ('half leaf finger'); Odontodactylus ('tooth finger'); Stenodactylus ('narrow finger') -deres, -dira: Origin: Ancient Greek: δέρη (dére). Meaning: neck, collar. Examples: Acanthoderes ('spiny neck'); Cryptodira ('hidden neck'); Pleurodira ('rib neck') -derm: Pronunciation: /dɜrm/. Origin: Ancient Greek: δέρμα (dérma). Meaning: animal hide. Used for skin. Examples: Placodermi ('plated skin'); Echinodermata ('hedgehog skin'); Ostracodermi ('shell skin'); Pachydermata ('thick skin') -delphys, -delphis, delpho-: Pronunciation: /dɜlfɪs/, /dɜlfʊ/. Origin: Ancient Greek: δελφύς ( delphis). Meaning: womb. Used for therian mammals. Examples: Sinodelphys ('Chinese womb'); Didelphis ('two womb'); Didelphodon ('two-womb [ie opossum] tooth'); Delphinus ('with a womb'); Monodelphis ('one womb') dendro-, -dendron, -dendrum: Pronunciation: /dɛn.dɹoʊ/, /ˈdɛndɹən/, /dɛndɹəm/. Origin: Ancient Greek: δένδρον (déndron). Meaning: tree. Examples: Rhododendron ('rose tree'); Liriodendron ('lily tree'); Dendrocnide ('tree nettle'); Epidendrum ('above tree'); Lepidodendron ('scaled tree'); Dendrobates ('tree climber'); Dendrocolaptes ('tree chiseller') di-: Pronunciation: /daɪ/. Origin: Ancient Greek: δίς (dís). Meaning: twice. Used to indicate two of something. Examples: Dilophosaurus ('two crested lizard'); Diceratops ('two-horned face'); diapsid ('two arches'); Didelphis ('two womb'); Dichrostigma ('two-colored brand'); Diprotodon ('two front teeth'); Diceros ('two horn'); Dipus ('two foot') dino-, deino-: Pronunciation: /daɪnoʊ/. Origin: Ancient Greek: δεινός (deinós). Meaning: 'terrible',


id: list-of-commonly-used-taxonomic-affixes-20260505-3
file: data/en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes-3.md
category: reference
title: List of commonly used taxonomic affixes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes
date_saved: 2026-05-05T08:20:49.524905+00:00
instance: kb-cron
parent: list-of-commonly-used-taxonomic-affixes-20260505-0
summary:
Examples: Dilophosaurus ('two-crested lizard'); Brachylophosaurus ('short-crested lizard'); Saurolophus ('lizard crest'); Teinolophos ('extended crest'); Lophoceros ('crest horn') lyco-: Pronunciation: /lɪkoʊ/. Origin: Ancient Greek: λύκος (lýkos). Meaning: wolf. Examples: Lycopodium ('wolf foot'); Lycodon ('wolf tooth'); Lycoperdon ('wolf fart') macro-: Pronunciation: /mækroʊ/. Origin: Ancient Greek: μακρός (makrós). Meaning: (correctly) long; (usually) large. Examples: macropod ('big foot'); Macrodontophion ('big tooth snake'); Macrogryphosaurus ('big enigmatic lizard') -maia, maia-: Pronunciation: /meiə/ Origin: Ancient Greek: Μαῖα (Maîa). Meaning: Originally the mother of Hermes in Greek mythology and the goddess of growth in Roman mythology, alternatively spelled Maja. Frequently used to indicate maternal roles, this word should not be construed as translating directly to 'mother' (Latin māter; Ancient Greek μήτηρ mḗtēr); aside from being a proper name, in Ancient Greek 'maîa' can translate to 'midwife' or 'foster mother' and was used as an honorific address for older women, typically translated into English as 'Good Mother'. Examples: Maiasaura ('Good Mother/Maia's lizard'); Eomaia ('dawn Maia'); Juramaia ('Jurassic Maia'); Maiacetus ('mother whale') mega-, megalo-: Pronunciation: /mɛga/, /mɛgaloʊ̯/. Origin: Ancient Greek: μέγας, μεγάλη (mégas, megálē). Meaning: big/great. Examples: Megarachne ('great spider'); Megalosaurus ('great lizard'); megalodon ('great tooth'); Megaloceros ('great horn') micro-: Pronunciation: /maɪkroʊ̯/. Origin: Ancient Greek: μικρός (mikrós). Meaning: 'small'. Examples: Microraptor


id: list-of-commonly-used-taxonomic-affixes-20260505-4
file: data/en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes-4.md
category: reference
title: List of commonly used taxonomic affixes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes
date_saved: 2026-05-05T08:20:49.524905+00:00
instance: kb-cron
parent: list-of-commonly-used-taxonomic-affixes-20260505-0
summary:
Used for early appearances in the fossil record. Examples: Protoceratops ('first horned face'); Protognathosaurus ('first jaw lizard'); Protohadros ('first hadrosaur') psittaco-, -psitta: Pronunciation: /sitɑːkoʊ/, /psitə/. Origin: Ancient Greek ψιττακός (psittakós). Meaning: parrot. 'Psittaco-' is used for parrot-like creatures, while the suffix 'psitta' is used for parrots. Examples: Psittacosaurus ('parrot lizard'); Cyclopsitta ('Cyclops parrot'); Xenopsitta ('strange parrot'); Psittaciformes ('parrot form') pter-, ptero-, -pterus, pteryg-, -ptera, -pteryx. Pronunciation: /ter/, /teroʊ/, /pterəs/, /terɪg/, /pterə/, /pterɪx/. Origin: Ancient Greek πτέρυξ, πτέρυγος (pterux, ptérugos). Meaning: wing, of a wing, respectively. Used for many winged creatures, but also expanded to mean 'fin', and used for many undersea arthropods. The suffix '-ptera' is also used in orders of winged insects. Examples: Brachypterygius ('short finned'); Brachyptera ('short wing'); Pteranodon ('toothless wing'); Pterodactylus ('winged finger'); Eurypterus ('wide wing' or fin); Pterygotus ('winged' or finned); Coleoptera ('sheathed wing'); Camaroptera ('arched wing'); Archaeopteryx ('ancient wing'); Stenopterygius ('narrow finned'); Lepidoptera ('scaled wing'); Chiroptera ('hand wing'); Dermoptera ('skin wing'); Raphidioptera ('needle wing'); Rhomboptera ('rhombus wing'); Orthoptera ('straight wing'); Mecoptera ('long wing'); Delphinapterus ('dolphin fin'); Megaloptera ('great wing'); Megaptera ('great fin'); Neopterygii ('new fin'); Titanoptera ('Titan wing'); Sarcopterygii ('flesh fin'); Actinopterygii ('ray fin'); Neuroptera ('net wing') -pus: see -pod, -podo-, -pus. -raptor, raptor-: Pronunciation:


id: list-of-commonly-used-taxonomic-affixes-20260505-5
file: data/en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes-5.md
category: reference
title: List of commonly used taxonomic affixes
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_commonly_used_taxonomic_affixes
date_saved: 2026-05-05T08:20:49.524905+00:00
instance: kb-cron
parent: list-of-commonly-used-taxonomic-affixes-20260505-0
summary:
Examples: Xenosmilus ('strange knife'); Xenotarsosaurus ('strange ankled lizard'); Xenopsitta ('strange parrot'); Xenocyon ('strange dog'); Xenokeryx ('strange horn'); Xenostega ('strange roof'); Xenozancla ('strange animal'); Xenodermus ('strange skin'); Xenopus ('strange foot'); Xenops ('strange face') -zoon, -zoa: Pronunciation: /zoʊɑːn/, /zoʊə/. Origin: Ancient Greek ζῷον (zōion). Meaning: animal. Used for broad categories of animals, or in certain names of animals. Examples: Metazoa ('encompassing animals'); Parazoa ('near animals'); Ecdysozoa ('moulting animals'); Yunnanozoon ('animal from Yunnan'); Yuyuanozoon ('animal from Yu Yuan'); Hydrozoa ('water animals'); Spermatozoon ('seed animal'); Echinozoa ('hedgehog animals'); Asterozoa ('star animals'); Trilobozoa ('three-lobed animals'); Placozoa ('plate animals'); Amoebozoa ('amoeba animals') == References == == See also == List of Latin and Greek words commonly used in systematic names List of Greek and Latin roots in English List of Latin words with English derivatives List of medical roots, suffixes and prefixes


id: list-of-u-s-state-fossils-20260505-0
file: data/en.wikipedia.org/wiki/List_of_U.S._state_fossils-0.md
category: reference
title: List of U.S. state fossils
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_U.S._state_fossils
date_saved: 2026-05-05T08:20:50.696926+00:00
instance: kb-cron
parent: list-of-u-s-state-fossils-20260505-0
summary:
Most states in the US have designated a state fossil, many during the 1980s. It is common to designate a fossilized species, rather than a single specimen or a category of fossils. State fossils are distinct from other state emblems like state dinosaurs, state stones, state minerals, state gemstones or state rocks and a state may designate one, a few, or all of those. For example, in Arizona, the state stone is turquoise and the state dinosaur is Sonorasaurus thompsoni yet the state fossil is petrified wood. The two first states to designate a state fossil were Nebraska and North Dakota, both in 1967. Six states and the District of Columbia as of March 10th, 2026 still lack an explicit state fossil: Arkansas: There is no state fossil in Arkansas, though the state designated Arkansaurus as its state dinosaur. District of Columbia: Capitalsaurus is the state dinosaur of Washington D.C., but the District has not chosen a state fossil. Florida: There is no state fossil in Florida, though agatised coral, which is a fossil, is the state stone. Hawaii: In history, Hawaii is too young to have many fossils, and its igneous composition makes fossils harder to find. The government


id: white-river-fauna-20260505-0
file: data/en.wikipedia.org/wiki/White_River_Fauna-0.md
category: reference
title: White River Fauna
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/White_River_Fauna
date_saved: 2026-05-05T08:20:52.012385+00:00
instance: kb-cron
parent: white-river-fauna-20260505-0
summary:
The White River Fauna are fossil animals found in the White River Group of South Dakota, North Dakota, Wyoming, Colorado and Nebraska in the United States. In southwest South Dakota and northwest Nebraska, these fossils are characteristic of the White River Badlands (including Badlands National Park), though they can be found far beyond the limits of the White River watershed. In Wyoming, the White River Group is undifferentiated, and is more commonly known as the White River Formation. Further east in Nebraska and South Dakota, the group is divided into the Chadron Formation (lower part) and Brule Formation (upper part). Exposures are less well-investigated in northeast Colorado and scattered sites across western North Dakota. The White River Group is overlain by the Sharps Formation in Badlands National Park and the Arikaree Group in northwest Nebraska. Animals from the White River Group date from the Eocene and Oligocene epochs. The fauna is representative of four North American Land Mammal Ages (NALMAs): Arikareean (late Oligocene - early Miocene, 29.5 - 18.5 million years ago) Whitneyan (mid-Oligocene, 31.8 - 29.5 million years ago) Orellan (early Oligocene, 33.9 - 31.8 million years ago) Chadronian (late Eocene, 37 - 33.9 million years ago) == Birds


id: list-of-philosophical-organizations-20260505-0
file: data/en.wikipedia.org/wiki/List_of_philosophical_organizations-0.md
category: reference
title: List of philosophical organizations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_philosophical_organizations
date_saved: 2026-05-05T08:20:54.796861+00:00
instance: kb-cron
parent: list-of-philosophical-organizations-20260505-0
summary:
This is a list of philosophical organizations and societies. Academia Analitica American Association of Philosophy Teachers American Catholic Philosophical Association American Ethical Union American Philosophical Association American Philosophical Society American Society for Aesthetics American Society for Political and Legal Philosophy Animal Rights Cambridge Arché (research center) Aristotelian Society Association for Logic, Language and Information Association for Symbolic Logic Association for the Scientific Study of Consciousness Australasian Association of Philosophy Batavian Society for Experimental Philosophy British Philosophical Association British Society for Ethical Theory British Society of Aesthetics Café Philosophique Cambridge Philosophical Society Canadian House of Commons Standing Committee on Access to Information, Privacy and Ethics Canadian Philosophical Association Canadian Society for History and Philosophy of Mathematics Carnegie Council for Ethics in International Affairs Center for Ethics at Yeshiva University Center for Religion, Ethics and Social Policy Center for the Study of Ethics in the Professions Centre de Recherche en Epistémologie Appliquée Centre for Applied Ethics Centre for Applied Philosophy and Public Ethics (CAPPE) Centre for History and Philosophy of Science, University of Leeds Charity International Citizens for Responsibility and Ethics in Washington Commission on Federal Ethics Law Reform Committee on Publication Ethics Computer Ethics Institute Concerned Philosophers for Peace Conscious enterprise


id: list-of-philosophies-20260505-0
file: data/en.wikipedia.org/wiki/List_of_philosophies-0.md
category: reference
title: List of philosophies
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_philosophies
date_saved: 2026-05-05T08:20:56.166227+00:00
instance: kb-cron
parent: list-of-philosophies-20260505-0
summary:
The following is a list of philosophies, schools of thought and philosophical movements. == A == Absurdism – Academic skepticism – Accelerationism - Achintya Bheda Abheda – Action, philosophy of – Actual idealism – Actualism – Advaita Vedanta – Aesthetic Realism – Aesthetics – African philosophy – Afrocentrism – Agential realism – Agnosticism – Agnostic theism – Ajātivāda – Ājīvika – Ajñana – Alexandrian school – Alexandrists – Ambedkarism – American philosophy – Analytical Thomism – Analytic philosophy – Anarchism – Ancient philosophy – Animism – Anomalous monism – Anthropocentrism – Antinatalism – Antinomianism – Antipositivism – Anti-psychiatry – Anti-realism – Antireductionism – Applied ethics – Archaeology, philosophy of – Aristotelianism – Arithmetic, philosophy of – Artificial intelligence, philosophy of – Art, philosophy of – Asceticism – Atheism – Atomism – Augustinianism – Australian realism – Authoritarianism – Averroism – Avicennism – Axiology – Aztec philosophy == B == Baptists – Bayesianism – Behaviorism – Bioconservatism – Biology, philosophy of – Biosophy – Bluestocking – Brahmoism – British idealism – Budapest School – Buddhist atomism – Buddhist philosophy – Business philosophy == C == Cambridge Platonists – Cambridge Ritualists – Capitalism – Carlyleanism – Carolingian Renaissance – Cartesianism – Categorical


id: list-of-philosophies-20260505-1
file: data/en.wikipedia.org/wiki/List_of_philosophies-1.md
category: reference
title: List of philosophies
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_philosophies
date_saved: 2026-05-05T08:20:56.166227+00:00
instance: kb-cron
parent: list-of-philosophies-20260505-0
summary:
== N == Naïve realism – Naturalism – Natural Science, philosophy of – Natural Supernaturalism – Nature, philosophy of – Nazism – Negative utilitarianism – Neo-Confucianism – Neoconservatism – Neo-Hegelianism – Neohumanism – Neoliberalism – Neo-Luddism – Neo-Kantianism – Neo-Marxism – Neo-medievalism – Neoplatonism – Neopositivism – Neopragmatism – Neopythagoreanism – Neoromanticism – Neo-Scholasticism – Neostoicism – Neotaoism – Neo Vedanta – Neuroethics – Neurophilosophy – Neuroscience, philosophy of – Neurotheology – Neutral monism – New Age – New Criticism – New Culture Movement – New Formalism – New humanism (literature) – New Life Movement – New realism – New Thought – Nichiren Buddhism – Nihilism – Nominalism – Non-cognitivism – Nondualism – Non-philosophy – Non-theism – Nyaya == O == Objective idealism – Objectivism – Occamism – Occasionalism – Olympism – Ontology – Ontotheology – Open individualism – Organicism – Oxford Calculators – Oxford Franciscan school == P == Paganism – Pakistani philosophy – Panbabylonism – Pancasila – Pancritical rationalism – Pandeism – Panentheism – Panpsychism – Pantheism – Pataphysics – Perception, philosophy of – Perennial philosophy – Perfectionism – Peripatetic school – Personalism – Perspectivism – Pessimism – Phenomenalism – Phenomenology – Philosophes – Philosophical anthropology – Philosophy,


id: the-void-in-art-and-media-20260505-0
file: data/en.wikipedia.org/wiki/The_Void_in_art_and_media-0.md
category: reference
title: The Void in art and media
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Void_in_art_and_media
date_saved: 2026-05-05T08:20:57.417985+00:00
instance: kb-cron
parent: the-void-in-art-and-media-20260505-0
summary:
Representation or portrayals of the notion of The Void can be found in popular culture: including visual art, performance art, music, literature and film and video games. In 2011, the Tate Museum in London presented an exhibition titled, Nothing Works: The Void, examining works that spanned over a century, including early 20th century works such as a 1918 work by the painter Kasimir Malevich, and a 1919 work by Marcel Duchamp, mid-century works by conceptual artist, Michael Asher, as well as late 20th century and early 21st-century contemporary artworks. In 2013, the Museum of Contemporary Art, Chicago hosted the exhibition, Destroy the Picture: Painting The Void, 1949-1962, featuring paintings that represented or referred to "the void." The exhibition included the work of 100 artists; the curatorial premise defined the concept of the void as "one of the most significant developments in contemporary abstract painting." The curators posit that artists were attracted to the subject as a result of an existential crisis after the use of the first atomic weapons in Japan during WWII. In 2020, the Museum of Modern Art, New York further developed the theme in the exhibition, Touching the Void, curated with works from the museum's permanent collection


id: index-of-physics-articles-20260505-0
file: data/en.wikipedia.org/wiki/Index_of_physics_articles-0.md
category: reference
title: Index of physics articles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Index_of_physics_articles
date_saved: 2026-05-05T08:20:58.869214+00:00
instance: kb-cron
parent: index-of-physics-articles-20260505-0
summary:
Physics (Greek: physis–φύσις meaning "nature") is the natural science which examines basic concepts such as mass, charge, matter and its motion and all that derives from these, such as energy, force and spacetime. More broadly, it is the general analysis of nature, conducted in order to understand how the world and universe behave. The index of physics articles is split into multiple pages due to its size. To navigate by individual letter use the table of contents below. == See also == List of basic physics topics == References ==


id: outline-of-physics-20260505-0
file: data/en.wikipedia.org/wiki/Outline_of_physics-0.md
category: reference
title: Outline of physics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Outline_of_physics
date_saved: 2026-05-05T08:21:00.100277+00:00
instance: kb-cron
parent: outline-of-physics-20260505-0
summary:
The following outline is provided as an overview of and topical guide to physics: Physics – natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves. == What type of subject is physics? == Physics can be described as all of the following: An academic discipline – one with academic departments, curricula and degrees; national and international societies; and specialized journals. A scientific field (a branch of science) – widely recognized category of specialized expertise within science, and typically embodies its own terminology and nomenclature. Such a field will usually be represented by one or more scientific journals, where peer-reviewed research is published. A natural science – one that seeks to elucidate the rules that govern the natural world using empirical and scientific methods. A physical science – one that studies non-living systems. A biological science – one that studies the role of physical processes in living organisms. See Outline of biophysics. == Branches == Astronomy – studies the universe beyond Earth, including its formation and development, and the evolution,


id: outline-of-physics-20260505-1
file: data/en.wikipedia.org/wiki/Outline_of_physics-1.md
category: reference
title: Outline of physics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Outline_of_physics
date_saved: 2026-05-05T08:21:00.100277+00:00
instance: kb-cron
parent: outline-of-physics-20260505-0
summary:
== History == History of physics – history of the physical science that studies matter and its motion through space-time, and related concepts such as energy and force Physics in the medieval Islamic world European science in the Middle Ages History of science and technology in China History of Indian science and technology === History of fields of physics === History of acoustics – history of the study of mechanical waves in solids, liquids, and gases (such as vibration and sound) History of agrophysics – history of the study of physics applied to agroecosystems History of astrophysics – history of the study of the physical aspects of celestial objects History of astronomy – history of the studies the universe beyond Earth, including its formation and development, and the evolution, physics, chemistry, meteorology, and motion of celestial objects (such as galaxies, planets, etc.) and phenomena that originate outside the atmosphere of Earth (such as the cosmic background radiation). History of astrodynamics – history of the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. History of astrometry – history of the branch of astronomy that involves precise measurements of the positions and


id: outline-of-physics-20260505-2
file: data/en.wikipedia.org/wiki/Outline_of_physics-2.md
category: reference
title: Outline of physics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Outline_of_physics
date_saved: 2026-05-05T08:21:00.100277+00:00
instance: kb-cron
parent: outline-of-physics-20260505-0
summary:
=== Ingredients === physical system - a collection of objects under study, physical observation - the study physical quantity - a quantified property of an object unit of measure - a standard quantity used to compare observations mathematical model - an abstract description of a system physical experiment - an intervention designed to test a model physical constant - a quantified property with no known model physical law - a broadly and thoroughly tested model === Basic principles === Physics – branch of science that studies matter and its motion through space and time, along with related concepts such as energy and force. Physics is one of the "fundamental sciences" because the other natural sciences (like biology, geology etc.) deal with systems that seem to obey the laws of physics. According to physics, the physical laws of matter, energy and the fundamental forces of nature govern the interactions between particles and physical entities (such as planets, molecules, atoms or the subatomic particles). Some of the basic pursuits of physics, which include some of the most prominent developments in modern science in the last millennium, include: Describing the nature, measuring and quantifying of bodies and their motion, dynamics etc. Newton's laws


id: list-of-accelerators-in-particle-physics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_accelerators_in_particle_physics-0.md
category: reference
title: List of accelerators in particle physics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_accelerators_in_particle_physics
date_saved: 2026-05-05T08:21:01.364848+00:00
instance: kb-cron
parent: list-of-accelerators-in-particle-physics-20260505-0
summary:
A list of particle accelerators used for particle physics experiments. Some early particle accelerators that more properly did nuclear physics, but existed prior to the separation of particle physics from that field, are also included. Although a modern accelerator complex usually has several stages of accelerators, only accelerators whose output has been used directly for experiments are listed. == Early accelerators == These all used single beams with fixed targets. They tended to have very briefly run, inexpensive, and unnamed experiments. === Cyclotrons === [1] The magnetic pole pieces and return yoke from the 60-inch cyclotron were later moved to UC Davis and incorporated into a 76-inch isochronous cyclotron which is still in use today === Other early accelerator types === === Synchrotrons === == Fixed-target accelerators == More modern accelerators that were also run in fixed target mode; often, they will also have been run as colliders, or accelerated particles for use in subsequently built colliders. === High intensity hadron accelerators (Meson and neutron sources) === === Electron and low intensity hadron accelerators === == Colliders == === Electron–positron colliders === === Hadron colliders === === Electron–proton colliders === == Light sources == == Hypothetical accelerators == Besides the


id: list-of-american-physical-society-prizes-and-awards-20260505-0
file: data/en.wikipedia.org/wiki/List_of_American_Physical_Society_prizes_and_awards-0.md
category: reference
title: List of American Physical Society prizes and awards
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_American_Physical_Society_prizes_and_awards
date_saved: 2026-05-05T08:21:02.547027+00:00
instance: kb-cron
parent: list-of-american-physical-society-prizes-and-awards-20260505-0
summary:
The American Physical Society gives out a number of awards for research excellence and conduct; topics include outstanding leadership, computational physics, lasers, mathematics, and more. == Prizes == === David Adler Lectureship Award in the Field of Materials Physics === The David Adler Lectureship Award in the Field of Materials Physics is a prize that has been awarded annually by the American Physical Society since 1988. The recipient is chosen for being "an outstanding contributor to the field of materials physics, who is noted for the quality of his/her research, review articles and lecturing." The prize is named after physicist David Adler with contributions to the endowment by friends of David Adler and Energy Conversion Devices, Inc. The winner receives a $5,000 honorarium. === Will Allis Prize for the Study of Ionized Gases === Will Allis Prize for the Study of Ionized Gases is awarded biannually "for outstanding contributions to understanding the physics of partially ionized plasmas and gases" in honour of Will Allis. The $10000 prize was founded in 1989 by contributions from AT&T, General Electric, GTE, International Business Machines, and Xerox Corporations. === Early Career Award for Soft Matter Research === This award recognizes outstanding and sustained contributions


id: list-of-american-physical-society-prizes-and-awards-20260505-1
file: data/en.wikipedia.org/wiki/List_of_American_Physical_Society_prizes_and_awards-1.md
category: reference
title: List of American Physical Society prizes and awards
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_American_Physical_Society_prizes_and_awards
date_saved: 2026-05-05T08:21:02.547027+00:00
instance: kb-cron
parent: list-of-american-physical-society-prizes-and-awards-20260505-0
summary:
=== Mildred Dresselhaus Prize in Nanoscience or Nanomaterials === Mildred Dresselhaus Prize in Nanoscience or Nanomaterials was first awarded in 2023. It honours the legacy of Mildred Dresselhaus, and is awarded for an "outstanding scientist in the areas of nanoscience or nanomaterials". The first recipient of the price was Eva Andrei. === George E. Duvall Shock Compression Science Award === George E. Duvall Shock Compression Science Award was established in 1987 "to recognize contributions to understanding condensed matter and non-linear physics through shock compression." It is awarded biannually. === Einstein Prize === The Einstein Prize was established in 1999 to recognize outstanding accomplishments in the field of gravitational physics. It is awarded in odd-numbered years. === Prize for a Faculty Member for Research in an Undergraduate Institution === Prize for a Faculty Member for Research in an Undergraduate Institution is awarded annually since 1986 to a "physicist whose research in an undergraduate setting has achieved wide recognition and contributed significantly to physics and who has contributed substantially to the professional development of undergraduate physics students". === Herman Feshbach Prize in Theoretical Nuclear Physics === The Herman Feshbach Prize in Theoretical Nuclear Physics was inaugurated in 2014 and is awarded annually


id: list-of-american-physical-society-prizes-and-awards-20260505-2
file: data/en.wikipedia.org/wiki/List_of_American_Physical_Society_prizes_and_awards-2.md
category: reference
title: List of American Physical Society prizes and awards
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_American_Physical_Society_prizes_and_awards
date_saved: 2026-05-05T08:21:02.547027+00:00
instance: kb-cron
parent: list-of-american-physical-society-prizes-and-awards-20260505-0
summary:
=== Lars Onsager Prize in Statistical Physics === The Lars Onsager Prize recognizes outstanding research in theoretical statistical physics including the quantum fluids. The prize consists of $10,000 as well as a certificate citing the contribution made by the recipient. It is presented annually, beginning in 1997. The prize was endowed in 1993 by Drs. Russell and Marian Donnelly in memory of Lars Onsager and his passion for analytical results. === Abraham Pais Prize for History of Physics === The Abraham Pais Prize for History of Physics is given jointly by the American Physical Society and the American Institute of Physics for "outstanding scholarly achievements in the history of physics". The prize, named after physicist and historian Abraham Pais, has been awarded annually since 2005. === George E. Pake Prize === The George E. Pake Prize was established in 1983 to recognize outstanding work by physicists combining original research accomplishments with leadership in the management of research or development in industry. The prize is presented biennially in even-numbered years. === Panofsky Prize in Experimental Particle Physics === The Panofsky Prize is an annual prize, established in 1985, given to recognize and encourage outstanding achievements in experimental particle physics. === Francis


id: list-of-second-moments-of-area-20260505-0
file: data/en.wikipedia.org/wiki/List_of_second_moments_of_area-0.md
category: reference
title: List of second moments of area
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_second_moments_of_area
date_saved: 2026-05-05T08:21:03.792918+00:00
instance: kb-cron
parent: list-of-second-moments-of-area-20260505-0
summary:
The following is a list of second moments of area of some shapes. The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. The unit of dimension of the second moment of area is length to fourth power, L4, and should not be confused with the mass moment of inertia. If the piece is thin, however, the mass moment of inertia equals the area density times the area moment of inertia. == Second moments of area == Please note that for the second moment of area equations in the below table: I x = ∬ A y 2 d x d y {\displaystyle I_{x}=\iint _{A}y^{2}\,dx\,dy} and I y = ∬ A x 2 d x d y . {\displaystyle I_{y}=\iint _{A}x^{2}\,dx\,dy.} == Parallel axis theorem == The parallel axis theorem can be used to determine the second moment of area of a rigid body about any axis, given the body's second moment of area about a parallel axis through the body's centroid, the area of the cross section, and the perpendicular distance (d) between the axes. I x


id: list-of-atmospheric-optical-phenomena-20260505-0
file: data/en.wikipedia.org/wiki/List_of_atmospheric_optical_phenomena-0.md
category: reference
title: List of atmospheric optical phenomena
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_atmospheric_optical_phenomena
date_saved: 2026-05-05T08:21:05.078924+00:00
instance: kb-cron
parent: list-of-atmospheric-optical-phenomena-20260505-0
summary:
Atmospheric optical phenomena include: Afterglow Airglow Alexander's band, the dark region between the two bows of a double rainbow. Alpenglow Anthelion Anticrepuscular rays Aurora (northern and southern lights, aurora borealis and aurora australis) Belt of Venus Brocken Spectre Circumhorizontal arc Circumzenithal arc Cloud iridescence Crepuscular rays Earth's shadow Earthquake lights Glories Green flash Halos, of Sun or Moon, including sun dogs Haze Heiligenschein or halo effect, partly caused by the opposition effect Ice blink Light pillar Lightning Mirages (including Fata Morgana) Monochrome Rainbow Moon dog Moonbow Nacreous cloud/Polar stratospheric cloud Rainbow Sprite (lightning) Subsun Sun dog Tangent arc Tyndall effect Upper-atmospheric lightning, including red sprites, Blue jets, and ELVES Water sky == See also == == References ==


id: list-of-baryons-20260505-0
file: data/en.wikipedia.org/wiki/List_of_baryons-0.md
category: reference
title: List of baryons
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_baryons
date_saved: 2026-05-05T08:21:06.625794+00:00
instance: kb-cron
parent: list-of-baryons-20260505-0
summary:
Baryons are composite particles made of three quarks, as opposed to mesons, which are composite particles made of an equal number of quarks and antiquarks. Baryons and mesons are both hadrons, which are particles composed solely of quarks or both quarks and antiquarks. The term baryon is derived from the Greek "βαρύς" (barys), meaning "heavy", because, at the time of their naming, it was believed that baryons were characterized by having greater masses than other particles that were classed as matter. Pentaquarks are exotic baryons composed of four quarks and one antiquark. In 2015, the LHCb collaboration at CERN definitively reported the observation of pentaquark states in the decay of bottom lambda baryons (Λ0b). Since then, additional pentaquark states have been discovered, including new observations in 2019 and 2022. While primarily created in laboratory conditions, pentaquarks might also form naturally during neutron star formation. Since baryons are composed of quarks, they participate in the strong interaction. Leptons, on the other hand, are not composed of quarks and as such do not participate in the strong interaction. The best known baryons are protons and neutrons, which make up most of the mass of the visible matter in the universe, whereas electrons,


id: list-of-centroids-20260505-0
file: data/en.wikipedia.org/wiki/List_of_centroids-0.md
category: reference
title: List of centroids
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_centroids
date_saved: 2026-05-05T08:21:09.084865+00:00
instance: kb-cron
parent: list-of-centroids-20260505-0
summary:
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object X {\displaystyle X} in n {\displaystyle n} -dimensional space is the intersection of all hyperplanes that divide X {\displaystyle X} into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of X {\displaystyle X} . For an object of uniform composition, or in other words, has the same density at all points, the centroid of a body is also its center of mass. In the case of two-dimensional objects shown below, the hyperplanes are simply lines. == 2-D Centroids == For each two-dimensional shape below, the area and the centroid coordinates ( x ¯ , y ¯ ) {\displaystyle ({\bar {x}},{\bar {y}})} are given: Where the centroid coordinates are marked as zero, the coordinates are at the origin, and the equations to get those points are the lengths of the included axes divided by two, in order to reach the center which in these cases are the origin and thus zero. == 3-D Centroids == For each three-dimensional body below, the volume and the centroid coordinates ( x ¯ , y ¯ , z ¯


id: list-of-cern-scientific-committees-20260505-0
file: data/en.wikipedia.org/wiki/List_of_CERN_Scientific_Committees-0.md
category: reference
title: List of CERN Scientific Committees
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_CERN_Scientific_Committees
date_saved: 2026-05-05T08:21:10.368207+00:00
instance: kb-cron
parent: list-of-cern-scientific-committees-20260505-0
summary:
Proposals for experiments are made at CERN and have to go through the correct channels in order to be approved. One of the last steps in the process is to submit the proposal to an appropriate CERN Scientific Committee. The committees will discuss the proposal and then pass on their recommendations to the Research Board (previously the Nuclear Physics Research Committee) for the final decision. Proposals approved become part of the CERN experimental programme. In 1960, John Adams, the Director General, created three committees to manage experiments for each bubble chamber experimental technique used at CERN. These replaced the previous Advisory and Bubble Chamber committees. At the end of the bubble chamber period, the system was again changed and based on machine, rather than experimental technique. The committees were changed and merged in order to accommodate to this. Since then, the committees have changed based on the creation and decommissioning of facilities and accelerators. == Current committees == == Past committees == == References ==


id: list-of-textbooks-on-classical-mechanics-and-quantum-mechanics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_textbooks_on_classical_mechanics_and_quantum_mechanics-0.md
category: reference
title: List of textbooks on classical mechanics and quantum mechanics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_textbooks_on_classical_mechanics_and_quantum_mechanics
date_saved: 2026-05-05T08:21:11.578852+00:00
instance: kb-cron
parent: list-of-textbooks-on-classical-mechanics-and-quantum-mechanics-20260505-0
summary:
This is a list of notable textbooks on classical mechanics and quantum mechanics arranged according to level and surnames of the authors in alphabetical order. == Undergraduate == === Classical mechanics === Feynman, Richard P. (2005). The Feynman Lectures on Physics. Vol. 1 (2nd ed.). Addison-Wesley. ISBN 978-0-8053-9065-0. Halliday, David; Resnick, Robert (1970). Fundamentals of Physics. John Wiley & Sons. Chapters 1–21. Numerous subsequent editions. Hamill, Patrick (2014). A Student's Guide to Lagrangians and Hamiltonians. Cambridge University Press. ISBN 978-1107617520. Hand, Louis; Finch, Janet (1998). Analytical Mechanics. Cambridge University Press. ISBN 0521573270. Kibble, T. W.; Berkshire, F. H. (2004). Classical Mechanics. Imperial College Press. ISBN 1860944248. Kleppner, Daniel; Kolenkow, Robert (1973). An Introduction to Mechanics. McGraw-Hill. ISBN 0-07-035048-5. Marion, Jerry; Thornton, Stephen (2003). Classical Dynamics of Particles and Systems (5th ed.). Brooks Cole. ISBN 0534408966. Morin, David (2005). Introduction to Classical Mechanics: With Problems and Solutions. Cambridge University Press. ISBN 9780521876223. Müller-Kirsten, Harald J.W. (2024). Classical Mechanics and Relativity (2nd ed.). World Scientific. ISBN 9789811287114. Taylor, John (2005). Classical Mechanics. University Science Books. ISBN 978-981-12-8711-4. Young, Hugh D.; Freedman, Roger A. (2019). University Physics with Modern Physics (15th ed.). Pearson. ISBN 978-0135159552. === Quantum mechanics === Eisberg, Robert; Resnick, Robert


id: list-of-common-physics-notations-20260505-0
file: data/en.wikipedia.org/wiki/List_of_common_physics_notations-0.md
category: reference
title: List of common physics notations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_common_physics_notations
date_saved: 2026-05-05T08:21:12.855715+00:00
instance: kb-cron
parent: list-of-common-physics-notations-20260505-0
summary:
This is a list of common physical constants and variables, and their notations. Note that bold text indicates that the quantity is a vector. == Latin characters == == Greek characters == == Other characters == == See also == List of letters used in mathematics and science Glossary of mathematical symbols List of mathematical uses of Latin letters Greek letters used in mathematics, science, and engineering Physical constant Physical quantity International System of Units ISO 31 == References ==


id: constant-resistance-network-20260505-0
file: data/en.wikipedia.org/wiki/Constant-resistance_network-0.md
category: reference
title: Constant-resistance network
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Constant-resistance_network
date_saved: 2026-05-05T08:21:14.149375+00:00
instance: kb-cron
parent: constant-resistance-network-20260505-0
summary:
A constant-resistance network in electrical engineering is a network whose input resistance does not change with frequency when correctly terminated. Examples of constant resistance networks include: Zobel network Lattice phase equaliser Boucherot cell Bridged T delay equaliser == References ==


id: list-of-physical-constants-20260505-0
file: data/en.wikipedia.org/wiki/List_of_physical_constants-0.md
category: reference
title: List of physical constants
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_physical_constants
date_saved: 2026-05-05T08:21:15.339487+00:00
instance: kb-cron
parent: list-of-physical-constants-20260505-0
summary:
The constants listed here are known values of physical constants expressed in SI units; that is, physical quantities that are generally believed to be universal in nature and thus are independent of the unit system in which they are measured. Many of these are redundant, in the sense that they obey a known relationship with other physical constants and can be determined from them. == Table of physical constants == == Uncertainties == While the values of the physical constants are independent of the system of units in use, each uncertainty as stated reflects our lack of knowledge of the corresponding value as expressed in SI units, and is strongly dependent on how those units are defined. For example, the atomic mass constant m u {\displaystyle m_{\text{u}}} is exactly known when expressed using the dalton (its value is exactly 1 Da), but the kilogram is not exactly known when using these units, the opposite of when expressing the same quantities using the kilogram. == Technical constants == Some of these constants are of a technical nature and do not give any true physical property, but they are included for convenience. Such a constant gives the correspondence ratio of a technical


id: list-of-contributors-to-general-relativity-20260505-0
file: data/en.wikipedia.org/wiki/List_of_contributors_to_general_relativity-0.md
category: reference
title: List of contributors to general relativity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_contributors_to_general_relativity
date_saved: 2026-05-05T08:21:16.610349+00:00
instance: kb-cron
parent: list-of-contributors-to-general-relativity-20260505-0
summary:
This is a dynamic list of persons who have made major contributions to the (mainstream) development of general relativity, as acknowledged by standard texts on the subject. Some related lists are mentioned at the bottom of the page. == A == Peter C. Aichelburg (Aichelburg–Sexl ultraboost, generalized symmetries), Miguel Alcubierre (numerical relativity, Alcubierre drives), Richard L. Arnowitt (ADM formalism), Abhay Ashtekar (Ashtekar variables, dynamical horizons) == B == Robert M L Baker, Jr. (high-frequency gravitational waves), James M. Bardeen (Bardeen vacuum, black hole mechanics, gauge-invariant linear perturbations of Friedmann-Lemaître cosmologies), Barry Barish (LIGO builder, gravitational-waves observation), Robert Bartnik (existence of ADM mass for asymptotically flat vacuums, quasilocal mass), Jacob Bekenstein (black hole entropy), Vladimir A. Belinsky (BKL conjecture, inverse scattering transform solution generating methods), Peter G. Bergmann (constrained Hamiltonian dynamics), Bruno Bertotti (Bertotti–Robinson electrovacuum, post-Minskowskian expansions), Jiří Bičák (exact solutions of the Einstein field equations), Heinz Billing (prototype of laser interferometric gravitational-wave detector), George David Birkhoff (Birkhoff's theorem), Hermann Bondi (gravitational radiation, Bondi radiation chart, Bondi mass–energy–momentum, LTB dust, maverick models), William B. Bonnor (Bonnor beam solution), Robert H. Boyer (Boyer–Lindquist coordinates), Vladimir Braginsky (gravitational-wave detector, quantum nondemolition (QND) measurement) Carl H. Brans (Brans–Dicke theory), Hubert Bray (Riemannian Penrose inequality),


id: list-of-contributors-to-general-relativity-20260505-1
file: data/en.wikipedia.org/wiki/List_of_contributors_to_general_relativity-1.md
category: reference
title: List of contributors to general relativity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_contributors_to_general_relativity
date_saved: 2026-05-05T08:21:16.610349+00:00
instance: kb-cron
parent: list-of-contributors-to-general-relativity-20260505-0
summary:
== N == Gernot Neugebauer (Neugebauer–Meinel dust disk solution), Ezra Ted Newman (Newman–Penrose formalism, Kerr–Newman black hole solution, Janis–Newman–Winicour solution, NUT vacuum, RT spacetimes, relation of lensing to Weyl tensor), Gunnar Nordström (Reissner–Nordström metric), Kenneth Nordtvedt (Nordtvedt effect, PPN formalism), Igor D. Novikov (Novikov chart in Schwarzschild vacuum, no-hair theorem, accretion disks around black holes, monograph) Yavuz Nutku Nutku-Halil solution for colliding waves, On the Nutku—Halil solution for colliding impulsive gravitational waves == O == Robert Oppenheimer (gravitational collapse, Oppenheimer–Volkoff limit, Tolman–Oppenheimer–Volkoff equation, Oppenheimer–Snyder model), Amos Ori (black hole interiors, mass inflation, shock singularity, time machines, radiation reaction, gravitational collapse) == P == Achilles Papapetrou (chart for Ernst vacuum family, Majumdar–Papapetrou electrovacuums, Dixon–Papapetrou equations), Paul Painlevé (Gullstrand–Painlevé coordinates), Roger Penrose (Hawking–Penrose singularity theorems, Penrose diagrams, techniques from algebraic geometry and differential topology, Penrose limits, cosmic censorship hypotheses, Penrose inequalities, geometry of gravitational plane waves, impulsive waves, Penrose–Khan colliding plane wave, Newman–Penrose formalism, Weyl curvature hypothesis, highly influential monograph), Alexei Zinovievich Petrov (Petrov classification of algebraic properties of Weyl curvature tensor), Tsvi Piran (gravitational collapse), Felix A. E. Pirani (gravitational radiation, Petrov–Pirani classification of algebraic properties of Weyl curvature tensor), Jerzy F. Plebański (Plebanski vacuum, Plebanski action), Eric Poisson (black hole


id: contributors-to-the-mathematical-background-for-general-relativity-20260505-0
file: data/en.wikipedia.org/wiki/Contributors_to_the_mathematical_background_for_general_relativity-0.md
category: reference
title: Contributors to the mathematical background for general relativity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Contributors_to_the_mathematical_background_for_general_relativity
date_saved: 2026-05-05T08:21:17.881640+00:00
instance: kb-cron
parent: contributors-to-the-mathematical-background-for-general-relativity-20260505-0
summary:
This is a list of contributors to the mathematical background for general relativity. For ease of readability, the contributions (in brackets) are unlinked but can be found in the contributors' article. == B == Luigi Bianchi (Bianchi identities, Bianchi groups, differential geometry) == C == Élie Cartan (curvature computation, early extensions of GTR, Cartan geometries) Elwin Bruno Christoffel (connections, tensor calculus, Riemannian geometry) Clarissa-Marie Claudel (Geometry of photon surfaces) == D == Tevian Dray (The Geometry of General Relativity) == E == Luther P. Eisenhart (semi-Riemannian geometries) Frank B. Estabrook (Wahlquist-Estabrook approach to solving PDEs; see also parent list) Leonhard Euler (Euler-Lagrange equation, from which the geodesic equation is obtained) == G == Carl Friedrich Gauss (curvature, theory of surfaces, intrinsic vs. extrinsic) == K == Martin Kruskal (inverse scattering transform; see also parent list) == L == Joseph Louis Lagrange (Lagrangian mechanics, Euler-Lagrange equation) Tullio Levi-Civita (tensor calculus, Riemannian geometry; see also parent list) André Lichnerowicz (tensor calculus, transformation groups) == M == Alexander Macfarlane (space analysis and Algebra of Physics) Jerrold E. Marsden (linear stability) == N == Isaac Newton (Newton's identities for characteristic of Einstein tensor) == R == Gregorio Ricci-Curbastro (Ricci tensor, differential geometry) Georg Bernhard


id: list-of-conversion-factors-20260505-0
file: data/en.wikipedia.org/wiki/List_of_conversion_factors-0.md
category: reference
title: List of conversion factors
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_conversion_factors
date_saved: 2026-05-05T08:21:19.219007+00:00
instance: kb-cron
parent: list-of-conversion-factors-20260505-0
summary:
This article gives a list of conversion factors for several physical quantities. A number of different units (some only of historical interest) are shown and expressed in terms of the corresponding SI unit. Conversions between units in the metric system are defined by their prefixes (for example, 1 kilogram = 1000 grams, 1 milligram = 0.001 grams) and are thus not listed in this article. Exceptions are made if the unit is commonly known by another name (for example, 1 micron = 10−6 metre). Within each table, the units are listed alphabetically, and the SI units (base or derived) are highlighted. The following quantities are considered: length, area, volume, plane angle, solid angle, mass, density, time, frequency, velocity, volumetric flow rate, acceleration, force, pressure (or mechanical stress), torque (or moment of force), energy, power (or heat flow rate), action, dynamic viscosity, kinematic viscosity, electric current, electric charge, electric dipole, electromotive force (or electric potential difference), electrical resistance, capacitance, magnetic flux, magnetic flux density, inductance, temperature, information entropy, luminous intensity, luminance, luminous flux, illuminance, radiation. == Length == == Area == == Volume == == Plane angle == == Solid angle == == Mass == Notes: See Weight for detail of


id: list-of-dualities-20260505-0
file: data/en.wikipedia.org/wiki/List_of_dualities-0.md
category: reference
title: List of dualities
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_dualities
date_saved: 2026-05-05T08:21:20.415568+00:00
instance: kb-cron
parent: list-of-dualities-20260505-0
summary:
== Mathematics == In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Alexander duality Alvis–Curtis duality Artin–Verdier duality Beta-dual space Coherent duality Conjugate hyperbola De Groot dual Dual abelian variety Dual basis in a field extension Dual bundle Dual curve Dual (category theory) Dual graph Dual group Dual object Dual pair Dual polygon Dual polyhedron Dual problem Dual representation Dual q-Hahn polynomials Dual q-Krawtchouk polynomials Dual space Dual topology Dual wavelet Duality (optimization) Duality (order theory) Duality of stereotype spaces Duality (projective geometry) Duality theory for distributive lattices Dualizing complex Dualizing sheaf Eckmann–Hilton duality Esakia duality Fenchel's duality theorem Grothendieck local duality Hodge dual Isbell duality Jónsson–Tarski duality Lagrange duality Langlands dual Lefschetz duality Local Tate duality Opposite category Poincaré duality Twisted Poincaré duality Poitou–Tate duality Pontryagin duality S-duality (homotopy theory) Schur–Weyl duality Series-parallel duality Serre duality Spanier–Whitehead duality Stone's duality Tannaka–Krein duality Verdier duality == Philosophy and religion == Dualism (philosophy of mind) Dualistic cosmology Epistemological dualism Soul dualism Yin and yang


id: lists-of-physics-equations-20260505-0
file: data/en.wikipedia.org/wiki/Lists_of_physics_equations-0.md
category: reference
title: Lists of physics equations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lists_of_physics_equations
date_saved: 2026-05-05T08:21:21.604017+00:00
instance: kb-cron
parent: lists-of-physics-equations-20260505-0
summary:
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only. == General scope == Variables commonly used in physics Continuity equation Constitutive equation == Specific scope == Defining equation (physical chemistry) List of equations in classical mechanics Table of thermodynamic equations List of equations in wave theory List of relativistic equations List of equations in fluid mechanics List of electromagnetism equations List of equations in gravitation List of photonics equations List of equations in quantum mechanics List of equations in nuclear and particle physics == See also == List of equations Operator (physics) Laws of science == Units and nomenclature == Physical constant Physical quantity SI units SI derived unit SI electromagnetism units List of common physics notations


