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It is purely incidental.
The rapport between a distance expressed in miles and the same distance in km is exactly 1.609344.
The rapport of consecutive fibonacci numbers tends (by continuing with the fibonacci serie) to 1.618033988749894848...
The two numbers differ of about 0.5%, half percent. Approximation of 0.5% is in facts quite good for many purposes.
That's also the error you will get if you convert big number km in miles with this method: you will always obtain 0.5% km more
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