#### Also known as Leonardo Pisano. Published ‘*Liber Abaci*’ in 1202.

1202 – Italy

‘A series of numbers in which each successive term is the sum of the preceding two’

For example: **1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 , 89 , 144….**

The series is known as the Fibonacci sequence and the numbers themselves as the Fibonacci numbers.

The Fibonacci sequence has other interesting mathematical properties – the ratio of successive terms ( larger to smaller; **1/1, 2/1, 3/2, 5/3, 8/5….** ) approaches the number **1.618**

This is known as the **golden ratio** and is denoted by the Greek letter Phi.

Phi was known to ancient Greeks.

Greek architects used the ratio **1:Phi** as part of their design, the most famous example of which is the Parthenon in Athens.

Phi also occurs in the natural world.

Flowers often have a Fibonacci number of petals.

During his travels in North Africa, Fibonacci learned of the decimal system of numbers that had evolved in India and had been taken up by the Arabs.

In his book *Liber Abaci* he re-introduced to Europe the Arabic numerals that we use today, adhering roughly to the recipe ‘the value represented must be proportional to the number of straight lines in the symbol’.

Following the Arabs, Fibonacci ( ‘son of the simpleton’ euph. or ‘son of the innocent’ ) introduced the place–value concept, with each position representing a different power of ten and these arranged in ascending order from right to left.

###### Related sites

- Fibonacci (maths.surrey.ac.uk)
- Evansville facullty (faculty.evansville.edu/ck6/bstud/fibo)