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As suggested elsewhere, this is more of a party trick then a practical approach to convert between km and miles.

The Wikipedia entry does suggest a greedy algorithm (at each step choosing the largest fib number that fits) though, using that we have

121 = 89 + 21 + 8 + 3

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I do think that it has practical applications for the smaller ratios that are easy to remember and/or derive. For example 5:8 is a both a closer approximation than 3:5 that most people use, and is more convenient when miles are a multiple of 5.

One problem with this is that it decomposes 2 * 55 to 89 + 21, etc which makes the conversion slightly harder than just converting 55 and doubling.

Also the decomposition of 88 is 55 + 21 + 8 + 3 + 1. A lot of terms just to find that phi * (Fn - 1) is (F{n+1} - 1) which isn't even very accurate.

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