Fibonacci/Golden ratio = 1.618 Kilometres in 1 mile = 1.609
Conversion is off by less than 1%, not bad at all
Yeah, it's nice an mysterious the first moment you hear about this but all the romance is gone once you think about how it works.
By far the most complicated part is the fact that the ratio of successive terms in the Fibonacci sequence approaches a specific number (which happens to be the golden ratio, which happens to be close to the ratio of km/mi).
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You only have to memorize how the fibbonaci sequence works, which is just addind the previous 2 numbers together to get the next
You only have to memorize ...
and have a lot of computing power available.
That algorithm ain't running itself.
Fun fact: If you have a scientific calculator (literal or app) but no other conversion tool available, the conversion factor between miles and kilometres is almost exactly ln 5. Disturbingly close in fact.
That's fewer keypresses than generating the Golden ratio or working out Fibonacci numbers. But if all you have is your head then, yeah, the Fibonacci trick is good enough in a pinch.
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There are many such ways to memorize conversion ratios. Admittedly, this one is particularly cool, since you can construct it from the fairly trivial fibonacci series. But I still feel, it's no replacement for the actual solution; get rid of imperial and adopt metric.