6.5 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Mathematical coincidence | 5/5 | https://en.wikipedia.org/wiki/Mathematical_coincidence | reference | science, encyclopedia | 2026-05-05T07:23:33.671306+00:00 | kb-cron |
The ratio of a mile to a kilometre is also approximately the golden ratio
φ
=
1
+
5
2
≈
1.618
.
{\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}\approx 1.618\,.}
As a consequence, a Fibonacci number of miles is approximately the next Fibonacci number of kilometres. The ratio of a mile to a kilometre is also very close to
ln
(
5
)
≈
1.6094379
,
{\displaystyle \ln(5)\approx 1.6094379,}
within 0.006%. This means that
5
m
≈
e
k
,
{\displaystyle 5^{m}\approx e^{k},}
where
m
{\displaystyle m}
is the number of miles,
k
{\displaystyle k}
is the number of kilometres and
e
{\displaystyle e}
is Euler's number. A density of one ounce per cubic foot is very close to one kilogram per cubic metre: 1 oz / ft3 = 0.028349523125 kg / (0.3048 m)3 ≈ 1.0012 kg/m3. The conversion factor between troy ounces and grams (1 troy ounce = 31.1034768 g) is approximately equal to
10
π
−
π
10
=
99
10
π
≈
31.1018
.
{\displaystyle 10\pi -{\frac {\pi }{10}}={\frac {99}{10}}\pi \approx 31.1018\,.}
==== Fine-structure constant ==== The fine-structure constant
α
{\displaystyle \alpha }
is close to, and was once conjectured to be precisely equal to 1/137. Its CODATA recommended value is
α
{\displaystyle \alpha }
= 1/137.035999177(21)
α
{\displaystyle \alpha }
is a dimensionless physical constant, so this coincidence is not an artifact of the system of units being used.
==== Earth's solar orbit ==== The number of seconds in one year, based on the Gregorian calendar, can be calculated by:
365.2425
(
days
year
)
×
24
(
hours
day
)
×
60
(
minutes
hour
)
×
60
(
seconds
minute
)
=
31
,
556
,
952
(
seconds
year
)
{\displaystyle 365.2425\left({\frac {\text{days}}{\text{year}}}\right)\times 24\left({\frac {\text{hours}}{\text{day}}}\right)\times 60\left({\frac {\text{minutes}}{\text{hour}}}\right)\times 60\left({\frac {\text{seconds}}{\text{minute}}}\right)=31,556,952\left({\frac {\text{seconds}}{\text{year}}}\right)}
This value can be approximated by
π
×
10
7
{\displaystyle \pi \times 10^{7}}
or 31,415,926.54 with less than one percent of an error:
[
1
−
(
31
,
415
,
926.54
31
,
556
,
952
)
]
×
100
=
0.4489
%
{\displaystyle \left[1-\left({\frac {31,415,926.54}{31,556,952}}\right)\right]\times 100=0.4489\%}
==== Proton-to-electron mass ratio ====
6
π
5
≈
1836.12
{\displaystyle 6\pi ^{5}\approx 1836.12}
is very close to the proton-to-electron mass ratio
μ
=
m
p
/
m
e
≈
1836.153
{\displaystyle \mu =m_{p}/m_{e}\approx 1836.153}
(a dimensionless constant), within 0.002%. When this was first pointed out in 1951, the most exact known value for
μ
{\displaystyle \mu }
was 1836.12, which differs from
6
π
5
{\displaystyle 6\pi ^{5}}
by just 0.0001%.
== See also == Almost integer Anthropic principle Birthday problem Exceptional isomorphism Experimental mathematics Koide formula Narcissistic number Sophomore's dream Strong law of small numbers
== References ==
== External links == (in Russian) В. Левшин. – Магистр рассеянных наук. – Москва, Детская Литература 1970, 256 с. Davis, Philip J. - Are There Coincidences in Mathematics - American Mathematical Monthly, vol. 84 no. 5, 1981. Hardy, G. H. – A Mathematician's Apology. – New York: Cambridge University Press, 1993, (ISBN 0-521-42706-1) Weisstein, Eric W. "Almost Integer". MathWorld. Various mathematical coincidences in the "Science & Math" section of futilitycloset.com Press, W. H., "Seemingly Remarkable Mathematical Coincidences Are Easy to Generate"