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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.

🤯

I knew this was coming 😂

@piggo @fribbledom metric weenies BTO

@piggo @fribbledom 1 mile is both 1 *and* 2 kilometres.

@uoou @piggo @fribbledom

Quantum fibonacci

@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.

@peemee @fribbledom Minus 40 above zero too.

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

@fribbledom but it's not coincidence?

@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

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

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.

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

@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.

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 ;-)

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

@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 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 φ's approximately one and a half, yes

@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 It doesn't, because in the limit the ratio of terms in the sequence approaches the Golden Ratio, which is 1.6180339..., while the miles/kilometres conversion is 1.609.

But it's pretty close ... certainly close enough for most purposes.

@ColinTheMathmo

Holy shit, that is cool. This is like mortys mindblowers!

@fribbledom

@fribbledom mind blown

@fribbledom What the hell?

@fribbledom mathematics is the language of the mage!

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

@sheogorath @fribbledom naw, if you want to talk bad measurements, lets talk ounces.

@matt @fribbledom Or british inches? 😂 https://www.youtube.com/watch?v=mmh819Lfgfs

@sheogorath @fribbledom At least the modern US Inch is precisely 25.4mm

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

@a @sheogorath @fribbledom yes

@matt

What about cubits?

@sheogorath @fribbledom

@sheogorath @matt @fribbledom Unless you're talking about Swedish miles, which is equal to 10 km.

Piggo 🌻@piggo@piggo.space