Monday, September 10, 2012

Conversion shortcut

Here's a math shortcut, new to me, from the very cool Futility Closet blog: you can use consecutive Fibonacci terms to convert miles to kilometers (and back, using the preceding Fibonacci numbers.) For example, 3 and 5. There are about 5 kilometers in 3 miles. To convert back, just reverse: there are about 3 miles in 5 kilometers. It's an estimate, good for figuring things on the fly, not exact.

And it works for numbers that are not Fibonacci numbers - express the original as a sum of Fibonacci numbers, do the conversion for each separately, and add them up. Here's an example from Peteris Krumins' coding blog:
For example, how many kilometers are there in 100 miles? Number 100 can be expressed as a sum of Fibonacci numbers 89 + 8 + 3. Now, the Fibonacci number following 89 is 144, the Fibonacci number following 8 is 13 and the Fibonacci number following 3 is 5. Therefore the answer is 144 + 13 + 5 = 162 kilometers in 100 miles. This is less than 1% off from the precise answer, which is 160.93 km.
And if you're interested, that blog also explains why it works.

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