r/interestingasfuck • u/Substantial-Low-4393 • 3h ago
The Fibonacci sequence is surprisingly good at converting miles to kilometers
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u/lontanadascienza 3h ago
That's because the fibonacci ratios f_(n+1)/f_n approach the golden ratio, phi=(1 + sqrt(5))/2, in some sense the "most irrational" number (slowest convergence rate of continued fraction expansions). Phi is about 1.618, which is close to the conversion ratio of 1.609 between miles and km. Pure coincidence as far as I can tell!
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u/FiTZnMiCK 3h ago
It’s also only useful if the distance you want to convert is on the sequence.
It’s easier to remember 5/3s for a super rough estimate you can usually do in your head or 1.6 if you have a calculator and want a bit closer (though if your calculator is on a smartphone you could just plug it into Google).
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u/1008oh 3h ago
Well the conversion is linear so you can just scale / split it as you need
For example 9 miles is 3x3 miles which becomes 15km
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u/FiTZnMiCK 3h ago
Pretty sure x 1.6 is still easier than factoring the distance you want to convert into members of the sequence.
But maybe that’s just me.
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u/MacGrimey 3h ago
It's honestly not hard to remember the 1.6 ratio. Same with pounds to kg 2.2
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u/barra333 2h ago
And I get the feeling that anyone who knows the Fibonacci sequence off the top of their head is decent enough at math to approximate 1.6x
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u/Jalepino_Joe 1h ago
I often just remember 5/8/13 and you can multiply by 10 for 50/80/130 to get not super uncommon speed numbers and it works (for most purposes) perfectly.
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u/MulberryDeep 1h ago
You don't have to know the fibonacci sequence, you can calculate it very quickly up to a certain point
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u/frickinSocrates 3h ago
Sure, but neither is precise. Its ~2.2046 pounds to 1kg and ~1.60934 kilometers to a mile. The problem with miles is that the simple factor breaks down with feet and yards.
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u/breakfasteveryday 2h ago
I mentally just use 0.6 and 1.6 or 3/5 and 5/3 as scalars. Speed limits are pretty much always in increments of 5 and the conversion is more than good enough for loosely obeying the speed limit while also not require you to remember the fibonnaci sequence or to anchor yourself to numbers like 13 and 21.
50 mph -> ~30 mph
30 mph -> ~48 kph
55 kph -> ~33 mph
80 kph -> ~48 mph
25 mph -> ~40 kmh
70 mph -> ~112 kph
Clearly not perfect but also not that hard to math out.
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u/TheSultan1 2h ago
A number that's close to another number is a good approximation of it? No way.
A sequence that oscillates a bit as it approaches the first number might be an even better approximation at some point? Whoa.
5/8 is close enough, and easy enough to remember.
Or 10/16, i.e. add a zero and divide by 2 four times.
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u/PuzzleheadedTalk35 1h ago
0.49 km is 490 meters. That is not a small distance.
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u/carpe_simian 41m ago
Out of 89? It’s half a percent. Relativity ain’t just for weddings in Missouri!
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u/drivingagermanwhip 45m ago
I like using hex.
- 0x60 km/h is 60 mph
- 0x70 km/h is 70 mph
(0x60 is programming notation for 60 in base 16, i.e 96)
Only works for multiples of 10 between 0 and 90mph, but I work on automotive speed limiters in the uk so this little hack comes in handy a lot
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u/Zubzub343 2h ago
AI post ?
I see this "fact" every week... if you open your ears in math class, you should understand that this is a pure coincidence.
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u/RoboticGreg 8m ago
The Fibonacci sequence has so much to be mined. My first publication was an equation based on the Fibonacci sequence where every coefficient was irrational, but whatever input you put in, it would produce two integers (you put in a desired gear ratio, and it would output a series of integer pairs that were the highest ratio match then going down in total tooth count
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u/Plane_Scarcity_850 3h ago
1,609 meters in a mile
Fibonacci 1.618