Example: 50 kilometers: Using the Fibonacci method: 50 = 34 + 13 + 3. Replace each of those Fibonacci numbers with the previous Fibonacci number, and voila: an approximate conversion from km to miles! So 50 km becomes 21 + 8 + 2 = 31 miles.

Note though that one could also just divide by 1.6, by dividing by 2 four times, and shuffling a decimal: 50 -> 25 -> 12.5 -> 6.25 -> 3.125 -> 31.25 miles.

Seems like a toss-up.

]]>Well, okay, so multiplying 50 by 1.6 in your head is pretty simple too (double it 4 times and shift a decimal), which gives you 80km, which is slightly more accurate.

But still, to have this sort of application of representations of numbers as sums of Fibonacci numbers, that’s the sort of thing that makes me say “I love mathematics”.

]]>34->55, 13->21, 3->5. After summing up the shifted ones you’ve got kilometers: 50mi is approximately 55+21+5=81km (in this case, this gives you less than 1% error, since the true value is approx. 80.4672km). (I learned this trick from “Concrete Mathematics” by Graham, Knuth and Patashnik – yes _that_ Knuth;) – a really geeky book, very hard to read (for me), but also very interesting). ]]>