# Mathematician:Leonardo Fibonacci

## Mathematician

Italian mathematician.

One of the most important figures in the history of the development of mathematics.

Wrote the highly influential and important *Liber Abaci* in which he discussed the Hindu-Arabic number system and its practical applications.

Most famous for the Fibonacci numbers. The number sequence itself was known to Indian mathematicians as early as the $6$th century, but it was Fibonacci's *Liber Abaci* which made them well-known throughout Europe.

## Nationality

Italian

## History

- Born: c. 1170
- Died: c. 1250

## Theorems and Definitions

- Fibonacci numbers
- Brahmagupta-Fibonacci Identity (with Brahmagupta) (also known as Diophantus's Identity)
- Practical Number (discussed at length in
*Liber Abaci*)

### Concepts derived from Fibonacci numbers

- Fibonacci Polynomial
- Fibonacci Prime
- Fibonacci String, also known as a Fibonacci Word
- Fibonacci Number System
- Fibonacci Nim
- Reciprocal Fibonacci Constant
- Pisano Period

Results named for **Leonardo Fibonacci** can be found here.

Definitions of concepts named for **Leonardo Fibonacci** can be found here.

## Publications

- 1202:
*Liber Abaci*(*Book of Abacus*or*Book of Calculation*) which introduced the Arabic numerals to the Western world. Sometimes (possibly erroneously) called*Liber Abbaci*. - 1220:
*Practica Geometriae*, a compendium on geometry and trigonometry. - 1225:
*Flos*, solutions to problems posed by a friend of his,**Johannes of Palermo**. - 1225:
*Liber Quadratorum*(*The Book of Squares*) on Diophantine equations, in which in particular the Brahmagupta-Fibonacci Identity is discussed. *Di minor guisa*, on commercial arithmetic (lost)- A commentary on Book X of Euclid's
*The Elements*(lost)

## Notable Quotes

*When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else.*- -- $1202$:
*Liber Abaci*

- -- $1202$:

## Critical View

*Fibonacci was by far the greatest European mathematician of the Middle Ages.*

## Also known as

**Leonardo Fibonacci** also known as **Leonardo of Pisa**, **Leonardo Pisano**, **Leonardo Bonacci** or usually just **Fibonacci**.

The name **Fibonacci** comes (posthumously) from **filius Bonacci**, that is: **son of Bonacci** (his father was nicknamed **Bonacci**, meaning **good-natured** or **simpleton**). These were the days before official surnames. The name is not recorded before the $18$th century and may have been invented as late as then.

An ironic soubriquet.

## Linguistic Note

**Fibonacci** is an Italian surname whose pronunciation is something like ** Fib-bo-nat-chi**, or

**, according to taste.**

*Fib*-bo-*nar*-chiAvoid pronouncing it ** Fie-bo-nac-ky**.

## Sources

- John J. O'Connor and Edmund F. Robertson: "Leonardo Fibonacci": MacTutor History of Mathematics archive

- 1926: Henry Ernest Dudeney:
*Modern Puzzles*... (previous) ... (next): Solutions: $92$. -- A Cow's Progeny - 1968: Henry Ernest Dudeney:
*536 Puzzles & Curious Problems*... (previous) ... (next): Answers: $175$. A Cow's Progeny - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $0$ Zero - 1992: David Wells:
*Curious and Interesting Puzzles*... (previous) ... (next): Liber Abaci - 1997: Donald E. Knuth:
*The Art of Computer Programming: Volume 1: Fundamental Algorithms*(3rd ed.) ... (previous) ... (next): $\S 1.2.8$: Fibonacci Numbers - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $0$ Zero - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Fibonacci,**also known as**Leonardo of Pisa**(*c.*1175-*c.*1250) - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Leonardo of Pisa** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Fibonacci,**also known as**Leonardo of Pisa**(*c.*1175-*c.*1250) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Leonardo of Pisa** - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $3$: Notations and Numbers: The Dark Ages? - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Fibonacci**(about 1170-1250) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Leonardo of Pisa**