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Leonardo of Pisa
Born	c. 1170 Pisa, Italy
Died	c. 1250

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".^[1]

Fibonacci is best known to the modern world for:^[2]

• 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.^[3]

Contents 1 Biography 2 Important publications 3 Liber Abaci 4 In popular culture 5 References 6 Bibliography 7 See also 8 External links

Leonardo was born in Pisa. His father Guglielmo was nicknamed Bonaccio ("good natured" or "simple"). Leonardo's mother, Alessandra, died when he was nine years old. Leonardo was posthumously given the nickname Fibonacci (derived from filius Bonacci, meaning son of Bonaccio).^[4]

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 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,^[5] 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 cloister of the Camposanto historical cemetery on the Piazza dei Miracoli.^[6]

• 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, devoted 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)

Main article: Liber Abaci

In his work, Fibonacci introduces the so-called modus Indorum (method of the Indians), today known as Hindu-Arabic numerals (Sigler 2003; Grimm 1973). The book advocated numeration with the digits 0–9 and place value. The book showed the practical importance of the new numeral system, using lattice multiplication and Egyptian fractions, by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interest, money-changing, and other applications. The book was well received throughout educated Europe and had a profound impact on European thought. Nevertheless, the use of decimal numerals did not become widespread until much later.^{[citation needed]}

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.

• Fibonacci's name was adopted by a Los Angeles-based art rock group, The Fibonaccis, that recorded from 1982-1987.
• A "word jazz" piece called "Fibonacci Numbers" was recorded by vocal artist Ken Nordine in 2001, referring in it to Fibonacci's life and work.
• Fibonacci and the Fibonnaci numbers are mentioned as a code to unlock a vessel at The DaVinci Code and The Da Vinci Code (film).
• Otto Fibonacci, a character from Prison Break, bears his surname.
• The Fibonacci Sequence is one of the key concepts used in the cult film, Pi: Faith in Chaos.
• The Fibonnaci Sequence is heavily used in the song "Lateralus" by Tool

1. ^ Howard Eves. An Introduction to the History of Mathematics. Brooks Cole, 1990: ISBN 0-03-029558-0 (6th ed.), p 261.
2. ^ Leonardo Pisano - page 3: "Contributions to number theory". Encyclopædia Britannica Online, 2006. Accessed 18 September 2006.
3. ^ Parmanand Singh. "Acharya Hemachandra and the (so called) Fibonacci Numbers". Math. Ed. Siwan , 20(1):28-30, 1986. ISSN 0047-6269]
4. ^ See the incipit of the Liber Abaci: "Incipit liber Abaci Compositus a leonardo filio Bonacij Pisano" (copied from the "Prologus" of the Liber Ab(b)aci at Latin Wikisource - emphasis added), in English: "Here starts the book of Calculation Written by leonardo son of Bonaccio, from Pisa"
5. ^ See the incipit of Flos: "Incipit flos Leonardi bigolli pisani..." (quoted in the MS Word document Sources in Recreational Mathematics: An Annotated Bibliography by David Singmaster, 18 March 2004 - emphasis added), in English: "Here starts 'the flower' by Leonardo the wanderer of Pisa..."
   The basic meanings of "bigollo" appear to be "good-for-nothing" and "traveller" (so it could be translated by "vagrant", "vagabond" or "tramp"). A. F. Horadam contends a connotation of "bigollo" is "absent-minded" (see first footnote of "Eight hundred years young"), which is also one of the connotations of the English word "wandering". The translation "the wanderer" in the quote above tries to combine the various connotations of the word "bigollo" in a single English word.
6. ^ Fibonacci's Statue in Pisa

• 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.

• Brahmagupta-Fibonacci identity
• Fibonacci heap

• Goetzmann, William N., Fibonacci and the Financial Revolution (October 23, 2003),Yale School of Management International Center for Finance Working Paper No. 03-28 [1]
• Charles Burnett, Leonard of Pisa (Fibonacci) and Arabic Arithmetic - the Medieval background to Fibonacci's work
• Fibonacci at Convergence
• 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