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Mind blown, I never realized this coincidence:

You can use the next number in the Fibonacci sequence (1 1 2 3 5 8 13 21 34) to convert from miles to kilometers.

For example, 13 miles is 21 kilometers.

🤯

@carcinopithecus @uoou @piggo @fribbledom ... and go backwards for kilometers to miles. This handy for small numbers where I remember the Fibonacci sequence, but with large ones I'll probably end up using significant digits to make them small numbers again.

@fribbledom I always forget I know this until I see it posted somewhere so I never remember to actually use it.

@fribbledom I remind myself when converting between °C and °F that 61 = 16 and 82 = 28.

@ipofanes @fribbledom Plus 40 below zero is the same temperature on both °F & °C.

@fribbledom Ya,some say Fibonacci proves existence of God!

@rayroy @fribbledom and they would be wrong. It works because the fibonacci radio (1.618) is close-ish to the ratio between miles and km (1.609). It's not a perfect conversion

@rayroy

Of course it is. The definition of the mile and the kilometer are entirely independent of each other, and yet...

@fribbledom
Lol for the sake of making you all crazy, I invite you to tumble down a ridiculous rabbit hole I tumbled down once upon a time. It was fun.
https://tobeornottobe.org/the-great-pyramid%e2%80%8b-intro/math-constants/ have fun lol don't go too crazy
@rayroy

@mistermonster
Until the 19th century, there were lots of different standards for the mile: for example, the Welsh mile is about 4 modern miles. I don't suppose the theories account for that...
@rayroy @fribbledom

@fribbledom @rayroy Technically not correct – a mile is defined through a metre: it is 1609.344 metres, that's the definition.
But they did evolve separately, I get your point. It's a fun coincidence.

@fribbledom wow, wtf. This works for quite a while before the Fibonacci numbers are slightly too low for the outputted kilometers.

WHAT IS HAPPENING

@fribbledom oh, okay, it’s because the golden ratio (1.618…) is very close to how many kilometers are in a mile (1.609…)

@fribbledom It works quite well as the ratio of consecutive numbers in the Fibonacci sequence converges to the golden ratio, which happens to be roughly 1.61803398874989484820, pretty close to the 1.6 conversion factor between miles and kilometers. Nice find :)

@sybren @fribbledom Miles to km, multiply by 1.609344. Any more decimal points are pointless.

@peemee @sybren @fribbledom Any more decimal places are not only pointless, they're also wrong unless they're all zero.

A yard is *defined* as 0.9144 m so multiplying by 1760 yards in a mile shows that 1.609344 km/mile is exact.

en.wikipedia.org/wiki/Internat

@edavies
Nah, the yard is defined as the length of that piece of brass in Trafalgar Square! 😉
@peemee @sybren @fribbledom

@peemee @fribbledom Miles are pointless. Just use SI like anyone else ;-)

@sybren @fribbledom that “nature is beautiful” meme, except with a golden ratio on a mph + km/h tachometer

@fribbledom It's not really a coincidence. The "closed form" for fibonacci numbers uses the golden ratio $(1+√{5}/2)^n$ which is roughly $1.6ⁿ$

@bremner @fribbledom yes, i convert from miles to kilometers using the x = 1 / (1+x) formula.

@bremner @fribbledom Well, it's sort of a coincidence that the ratio of kilometers to miles is very close to the golden ratio.

@bremner @fribbledom I /really/ appreciate this came from an instance called Mathstodon 🤓🔢🔣

@bremner @fribbledom It is a coincidence that the entirely arbitrary units of mile and kilometer have a ratio close to the mathematical concept of the golden ratio.

@fribbledom This is because phi, the golden ratio, is about 1.618, and the ratio of miles to kilometers is about 1.609.

@fribbledom That's awesome, i looked up why specifically and it's because the Golden Ratio is 1.618 and the number of kilometers in a mile is 1.609

@fribbledom After some ipython calculations, I find this to be true (0.618... vs 0.6214). Huh.

@fribbledom it's because kilometers to miles is around 0.621, very close to the golden ratio 0.618 I guess?

@fribbledom
I would assume it gets more accurate the further into the sequence you go?

@Scrith @fribbledom
Actually it does not. Have a look at the sequence of ratios:

2/1 = 2.0
3/2 = 1.5
5/3 = 1.666...
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615...
34/21 = 1.619...

You'll see that the sequence of ratios approximates the golden ratio (1.618...). But it does so non-monotonically, in a chaotic or oscillating fashion, sometimes closer to the conversion factor 1.6, sometimes further away from it.

The sequence of fibonacci _ratios_ can be split into two: One sequence with all elements with an odd index and the other only with even. Based on the numbers above:

2.0, 1.666..., 1.625, 1.619..., ...
and
1.5, 1.6, 1.615..., ...

This is just a guess, but maybe both sequences approach the golden ratio monotonically. (A proof for or against is possible.)

@Scrith Then indeed the first sequence above would only get closer 1.6, i.e. the observation by @fribbledom would only increase in accuracy.

@floppy
Hmm...interesting. Man, mathematics has so many fascinating facets
@fribbledom

@Scrith The disparity settles rather quickly to be 0.56% away from the actual answer
@fribbledom

@Scrith @fribbledom The ratio between consecutive numbers is oscillating, but converges to 1.6180339887.. which is further away from say 55/34 = 1.61764..

@fribbledom Not quite. 1 mile is approximately 1.6km, so there is quite a bit of rounding error involved, and this breaks down as the Fibonacci sequence gets bigger. But for the most part its close enough

@fribbledom If you want a precise conversion, 1 mile is precisely equal to 1.609344km ;)

@matt @fribbledom ~1.8 kilometers if we talk about nautical miles. I mean, mile is just a bad unit :X

@matt @fribbledom "My house was XXX inches tall before the great fire of London and YYY inches after the great fire of london." "Oh did it burn down?" "No, the inch burned down and was changed."

@matt @sheogorath @fribbledom Which ones? British or US? Weight or volume? Troy or avoirdupois?

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