Skip to content # Trail talk: Playing with numbers

The Fibonacci Sequence- useful maths for hiking

The Fibonacci Sequence is the series of numbers where the next number is found by adding up the two numbers before it. A simple sequence-

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, et al…

Living in the UK, the default unit of distance for Three Points of the Compass is the mile, however many people prefer to work with kilometres. I agree that it is a much handier unit. But how to convert the one to the other? With an acceptance of a small (very small) margin of error, the Fibonacci Sequence is a pretty useful aid. Look at the numbers above.

There are eight kilometres in five miles (precisely- 8.04672 kilometres), and conversely, five miles in eight kilometres. It continues, fifty five miles equates to eighty nine miles (OK- 88.5139, but near enough).

If you want to convert a number that is not in the sequence, simply add together numbers in the sequence that total the required distance. i.e. if I have a distance of forty five miles to cover over a couple of days, this could be broken down into 21 + 21 + 3 from the Fibonacci Sequence. This gives me 34 + 34 + 5 = 73. Actually forty five miles equals 72.4205 kilometres exactly, so a pretty good fit. And remember, this also works in reverse. The answer is never more than half a percent out from true distance.

A handy bit of math, isn’t it?