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.
π€―
@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 Β°C and Β°F that 61 = 16 and 82 = 28.
@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 :)
@fribbledom It's not really a coincidence. The "closed form" for fibonacci numbers uses the golden ratio $(1+β{5}/2)^n$ which is roughly $1.6βΏ$
@fribbledom After some ipython calculations, I find this to be true (0.618... vs 0.6214). Huh.
@fribbledom
I would assume it gets more accurate the further into the sequence you go?
@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
Yes, I learned that a few years (?) ago! I think it's something that #fediverseToldMe !
The interesting question here of course is what lead to the unit for a mile and the unit for a kilometer having a relationship that closely approximates the golden ratio?
My hypothesis is that among the host of different definitions of the mile (as there were and are many), the one that won out and "felt right" reflected an approximation of the golden ratio since humans generally see the golden ratio as elegant and correct.
The interesting question here of course is what lead to the unit for a mile and the unit for a kilometer having a relationship that closely approximates the golden ratio?
My hypothesis is that among the host of different definitions of the mile (as there were and are many), the one that won out and "felt right" reflected an approximation of the golden ratio in relation to the kilometer since humans generally see the golden ratio as elegant and correct.
@fribbledom Calculating the fibonacci sequence is one of the most complex operations my breadboard CPU is capable of doing within its 16 byte of RAM.
You just accidentally gave it a functional purpose!
@fribbledom It is a neat coincidence.
But since the reason it works has to do with how close the conversion factor for miles -> km is to the golden ratio (GR) , it makes me wonder if the initial creation of the mile as a distance was intuitive as a GR distance.
The GR is everywhere.
@fribbledom hey, just checking in to see if forty people have told you about the golden ratio yet
@fribbledom It is, at best, an approximation with a significant error.
1 mile is neither 1km nor 2km, for example.
Depends *which* mile, as there's like a dozen of them, just as pounds, inches, ounces and gallons πIn contrast, there's just one definition of kilometer.
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oh, I had not realized ...
that said: How often do you need to convert numbers which are also Fibinacci numbers? I just use 8/5=1.6, which is off by about the same amount as the Golden Ratio (1.61803.....), but is much easier to apply in your head, particularly to the kind of rounded numbers you ususally encounter on road signs.
correct ratio is ~1.609 km/mile
@fribbledom nope, fibonacci is exponential, miles to kilometers is a constant ;)
will only work by coincidence in a small margin
@fribbledom that is basically due to the near similarity between the golden ratio and mile to kilometer conversion ratio!
Of course it is. The definition of the mile and the kilometer are entirely independent of each other, and yet...
@fribbledom What magic is this. That's cool!
