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Fibonacci, Leonardo, b. c.1170, d. after 1240, Italian mathematician, known also as Leonardo da Pisa. In *Liber abaci* (1202, 2d ed. 1228), for centuries a standard work on algebra and arithmetic, he advocated the adoption of Arabic notation. In *Practica geometriae* (1220) he organized and extended the material then known in geometry and trigonometry. The sequence of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, … , formed by adding consecutive members, is named for him; it occurs in higher mathematics in various connections. Baldassare Boncompagni edited his works (2 vol., 1857-62).

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

Leonardo of Pisa (c. 1170 – c. 1250), also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented mathematician of the Middle Ages".

Fibonacci is best known to the modern world for:

- The spreading of the Hindu-Arabic numeral system in Europe, primarily through the publication in the early 13th century of his Book of Calculation, the Liber Abaci.
- A modern number sequence named after him known as the Fibonacci numbers, which he did not discover but used as an example in the Liber Abaci.

Guglielmo directed a trading post (by some accounts he was the consultant for Pisa) in Bugia, a port east of Algiers in the Almohad dynasty's sultanate in North Africa (now Bejaia, Algeria). As a young boy, Leonardo traveled there to help him. This is where he learned about the Hindu-Arabic numeral system.

Recognizing that arithmetic with Hindu-Arabic numerals is simpler and more efficient than with Roman numerals, Fibonacci traveled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. Leonardo returned from his travels around 1200. In 1202, at age 32, he published what he had learned in Liber Abaci (Book of Abacus or Book of Calculation), and thereby introduced Hindu-Arabic numerals to Europe.

Leonardo became an amicable guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honoured Leonardo, referred to as Leonardo Bigollo, by granting him a salary.

In the 19th century, a statue of Fibonacci was constructed and erected in Pisa. Today it is located in the western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli.

Liber Abaci also posed, and solved, a problem involving the growth of a hypothetical population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century, but it was Fibonacci's Liber Abaci that introduced it to the West.

The higher up in the sequence, the closer two consecutive numbers of the sequence divided by each other will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1).

- Fibonacci's name was adopted by a Los Angeles-based art rock group, The Fibonaccis, that recorded from 1982-1987.
- Fibonacci and the Fibonacci numbers are mentioned as a code to unlock a vessel in Dan Brown's best selling novel, The DaVinci Code, and its movie adaptation.
- A youthful Fibonacci is one of the main characters in the novel Crusade in Jeans (1973). He was left out of the 2006 movie version, however.

- Liber Abaci (1202), a book on calculations (English translation by Laurence Sigler, Springer, 2002)
- Practica Geometriae (1220), a compendium on geometry and trigonometry.
- Flos (1225), solutions to problems posed by Johannes of Palermo
- Liber quadratorum, ("The Book of Squares") on Diophantine equations, dedicated to Emperor Frederick II. See in particular Fibonacci's identity.
- Di minor guisa (on commercial arithmetic; lost)
- Commentary on Book X of Euclid's Elements (lost)

- Acharya Hemachandra
- Brahmagupta–Fibonacci identity
- Carmichael's theorem
- Casey Mongoven
- Egyptian fraction
- Elliott wave principle
- Engel expansion
- Fibonacci coding
- Fibonacci family
- Fibonacci heap
- Fibonacci prime
- Fibonacci search technique
- Golden ratio
- Hylomorphism (computer science)
- Lagged Fibonacci generator
- Lucas number
- Negafibonacci
- NegaFibonacci coding
- Pisano period
- Practical number
- Primefree sequence
- Reciprocal Fibonacci constant
- Retracement
- Verner Emil Hoggatt, Jr.
- Virahanka
- Viswanath's constant
- Zeckendorf's theorem

- Goetzmann, William N. and Rouwenhorst, K.Geert, The Origins of Value: The Financial Innovations That Created Modern Capital Markets (2005, Oxford University Press Inc, USA), ISBN 0195175719.
- Grimm, R. E., "The Autobiography of Leonardo Pisano", Fibonacci Quarterly, Vol. 11, No. 1, February 1973, pp. 99-104.
- A. F. Horadam, "Eight hundred years young," The Australian Mathematics Teacher 31 (1975) 123-134.

- Who was Fibonacci? by Ron Knott.
- Goetzmann, William N., Fibonacci and the Financial Revolution (October 23, 2003), Yale School of Management International Center for Finance Working Paper No. 03-28
- Charles Burnett, Leonard of Pisa (Fibonacci) and Arabic Arithmetic - the Medieval background to Fibonacci's work
- Fibonacci at Convergence
- wallstreetcosmos.com, Fibonacci numbers and stock market analysis, (2008).
- O'Connor, John J and Robertson, Edmund F "Leonardo Pisano Fibonacci – 1170 - 1250" in The MacTutor History of Mathematics archive University of St Andrews website, Scotland, 1998.
- Liber Abaci and its Egyptian fraction methods

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This article is licensed under the GNU Free Documentation License.

Last updated on Friday October 10, 2008 at 05:02:51 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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