# Fibonacci

Italian mathematician (c. 1175)
(Redirected from Leonardo of Pisa)

Fibonacci, also known as Leonardo Bonacci, Leonardo Fibonacci and Leonardo of Pisa, lived c. 1170–1250. He was an Italian mathematician.[1] He was thought "the most talented Western mathematician of the Middle Ages".[2][3]

Statue of Fibonacci by Giovanni Paganucci in the Camposanto di Pisa, 1863

Fibonacci popularized the Hindu–Arabic numeral system to the Western World.[4] He did this in his composition in 1202 of Liber Abaci (Book of Calculation).[5] He also introduced to Europe the sequence of Fibonacci numbers which he used as an example in Liber Abaci.[6]

## Fibonacci number sequence

Fibonacci is best known for the list of numbers called the Fibonacci Sequence. The list never stops, but it starts this way:

```1,  1,  2,  3,  5,  8,  13,  21,  34,  55,  89, 144,  233,
377,  610,  987,  1597,  2584...
```

In this list, a person can find the next number by adding the last two numbers together.

```1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
34 + 55 = 89
55 + 89 = 144
89 + 144 = 233
144 + 233 = 377
233 + 377 = 610
377 + 610 = 987
610 + 987 = 1597
987 + 1597 = 2584
etc...
```

This series is also interesting because the ratio of two adjacent numbers in the series approaches the golden ratio.[7]

## References

1. "The Fibonacci Series – Biographies – Leonardo Fibonacci (ca.1175 – ca.1240)". Library.thinkquest.org. Archived from the original on 2010-02-05. Retrieved 2010-08-02.
2. Eves, Howard. An Introduction to the History of Mathematics. Brooks Cole, 1990: ISBN 0-03-029558-0 (6th ed.), p 261.
3. "Fibonacci Numbers". www.halexandria.org.
4. Leonardo Pisano – page 3: "Contributions to number theory". Encyclopædia Britannica Online, 2006. Retrieved 18 September 2006.
5. Singh, Parmanand. "Acharya Hemachandra and the (so called) Fibonacci Numbers". Math. Ed. Siwan , 20(1):28–30, 1986. ISSN 0047-6269]
6. Livio, Mario. (2003). The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, pp. 96-97.