3.3 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Liber Abaci | 1/2 | https://en.wikipedia.org/wiki/Liber_Abaci | reference | science, encyclopedia | 2026-05-05T08:45:28.580605+00:00 | kb-cron |
The Liber Abaci or Liber Abbaci (Latin for "The Book of Calculation") was a 1202 Latin work on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci. It is primarily famous for introducing both base-10 positional notation and the symbols known as Arabic numerals in Europe.
== Premise == Liber Abaci was among the first Western books to describe the Hindu–Arabic numeral system and to use symbols resembling modern "Arabic numerals". By addressing the applications of both commercial tradesmen and mathematicians, it promoted the superiority of the system and the use of these glyphs. Although the book's title is sometimes translated as "The Book of the Abacus", Sigler (2002) notes that the word in title does not refer to the abacus as a calculating device. Rather, the word "abacus" was used at the time to refer to calculation in any form; the spelling "abbacus" with two "b"s was, and still is in Italy, used to refer to calculation using Hindu-Arabic numerals. The book describes methods of doing calculations without aid of an abacus, and as Ore (1948) confirms, for centuries after its publication the algorismists (followers of the style of calculation demonstrated in Liber Abaci) remained in conflict with the abacists (traditionalists who continued to use the abacus in conjunction with Roman numerals). Carl Boyer emphasizes in his History of Mathematics that although "Liber abaci...is not on the abacus" per se, nevertheless "...it is a very thorough treatise on algebraic methods and problems in which the use of the Hindu-Arabic numerals is strongly advocated."
== Summary of sections == The first section introduces the Hindu–Arabic numeral system, including its arithmetic and methods for converting between different representation systems. This section also includes the first known description of trial division for testing whether a number is composite and, if so, factoring it. The second section presents examples from commerce, such as conversions of currency and measurements, and calculations of profit and interest. The third section discusses a number of mathematical problems; for instance, it includes the Chinese remainder theorem, perfect numbers and Mersenne primes as well as formulas for arithmetic series and for square pyramidal numbers. Another example in this chapter involves the growth of a population of rabbits, where the solution requires generating a numerical sequence. Although the resulting Fibonacci sequence dates back long before Leonardo, its inclusion in his book is why the sequence is named after him today. The fourth section derives approximations, both numerical and geometrical, of irrational numbers such as square roots. The book also includes proofs in Euclidean geometry. Fibonacci's method of solving algebraic equations shows the influence of the early 10th-century Egyptian mathematician Abū Kāmil Shujāʿ ibn Aslam.
== Fibonacci's notation for fractions == In Liber Abaci, Fibonacci's notation for rational numbers is intermediate in form between the Egyptian fractions commonly used until that time and the vulgar fractions still in use today. It differs from modern fraction notation in three key ways: