The Fibonacci Sequence is a very famous sequence of numbers, named after Italian mathematician Leonardo Fibonacci (though the sequence had already been described by Indian mathematicians). Each term in the sequence is composed of the sum of the previous two terms:
F = 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on …
As the sequence grows longer the ratio of each term to the previous term becomes closer and closer to the golden ratio of 1.618 (to four significant figures). This is helpful because the ratio of kilometres to miles is 1.609, which differs by only 0.556 percent.
Therefore, to quickly convert from miles to kilometres you only need to find the value in miles in the Fibonacci sequence and look at the next number in the sequence: 21 miles is 34 kilometres, 34 miles is 55 kilometres and so on. If converting in the other direction, look at the previous term to convert from kilometres to miles.