# Two Fascinating Properties of the Fibonacci Sequence

## There is no better way to learn mathematical induction than to work with the Fibonacci sequence

The Fibonacci sequence is a very well known and studied sequence of numbers which is often used in schools and in recreational mathematics because it can easily be understood by those with a limited technical mathematics education. The sequence is defined as follows: the first term is zero, the second term is one, and any other term is the sum of the prior two terms in the sequence. The sequence is written formally as follows:

for *n* > 1. The first ten terms of the sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.

There is plenty of evidence that these numbers were known over 2000 years ago as part of the Sanskrit poetic tradition. In Europe, the sequence first appeared in Fibonacci’s book *Liber Abaci* in 1202, where he used it to model a population of rabbits. Nowadays, the sequence has applications in many fields including economics, optics and financial market trading.

Page from Liber Abaci (1202) showing the Fibonacci sequence in the right margin