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Fibonacci

Fibonacci

definition : Fibonacci

Fibonacci (c. 1175 – c. 1250) was a mathematician from the Republic of Pisa in what is now Italy, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, "Fibonacci" (), was made up in 1838 by the French historian Guillaume Libri and is short for "filius Bonacci" ("son of (the) Bonacci") and he is also known as Leonardo Bonacci, Leonardo of Pisa, Leonardo Pisano Bigollo, or Leonardo Fibonacci. Fibonacci popularized the Hindu–Arabic numeral system in the Western World primarily through his composition in 1202 of Liber Abaci (Book of Calculation). He also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in Liber Abaci.

==History==

Fibonacci was born around 1175 to Guglielmo, a wealthy Italian merchant and, by some accounts, the consul for Pisa. Guglielmo directed a trading post in Bugia, a port in the Almohad dynasty's sultanate in North Africa. Fibonacci travelled with him as a young boy, and it was in Bugia (now Béjaïa, Algeria) that he learned about the Hindu–Arabic numeral system. by granting him a salary in a decree that recognized him for the services that he had given to the city as an advisor on matters of accounting and instruction to citizens.

The date of Fibonacci's death is not known, but it has been estimated to be between 1240 and 1250, most likely in Pisa.

==Liber Abaci (1202)==

In the Liber Abaci (1202), Fibonacci introduced the so-called modus Indorum (method of the Indians), today known as Hindu-Arabic numerals. The book advocated numeration with the digits 0–9 and place value. The book showed the practical use and value of the new Arabic numeral system by applying the numerals to commercial bookkeeping, converting weights and measures, calculation of interest, money-changing, and other applications. The book was well-received throughout educated Europe and had a profound impact on European thought. No copies of the 1202 edition are known to exist.

The second section explains the uses of Arabic numerals in business, for example converting different currencies, and calculating profit and interest, which were important to the growing banking industry. The book also discusses irrational numbers and prime numbers.

In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers. Fibonacci began the sequence not with 0, 1, 1, 2, as modern mathematicians do but with 1,1, 2, etc. He carried the calculation up to the thirteenth place (fourteenth in modern counting), that is 233, though another manuscript carries it to the next place: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377. Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence.

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

There are many mathematical concepts named after Fibonacci because of a connection to the Fibonacci numbers. Examples include the Brahmagupta–Fibonacci identity, the Fibonacci search technique, and the Pisano period. Beyond mathematics, namesakes of Fibonacci include the asteroid 6765 Fibonacci and the art rock band The Fibonaccis.

==Works== * Liber Abaci (1202), a book on calculations (English translation by Laurence Sigler, 2002) * Practica Geometriae (1220), a compendium of techniques in surveying, the measurement and partition of areas and volumes, and other topics in practical geometry (English translation by Barnabas Hughes, Springer, 2008). * 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 congruum and the Brahmagupta–Fibonacci identity. * Di minor guisa (on commercial arithmetic; lost) * Commentary on Book X of Euclid's Elements (lost)

==See also== * Fibonacci numbers in popular culture * Republic of Pisa

==References==

==Further reading== * * 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), . * Goetzmann, William N., [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=461740 Fibonacci and the Financial Revolution] (October 23, 2003), Yale School of Management International Center for Finance Working Paper No. 03–28 * Grimm, R. E., "[http://www.fq.math.ca/Scanned/11-1/grimm.pdf The Autobiography of Leonardo Pisano]", Fibonacci Quarterly, Vol. 11, No. 1, February 1973, pp. 99–104. * Horadam, A. F. "Eight hundred years young," The Australian Mathematics Teacher 31 (1975) 123–134. * Gavin, J., Schärlig, A., extracts of Liber Abaci online and analyzed on [http://www.bibnum.education.fr/mathematiques/algebre/leonard-de-pise-un-sujet-anodin-devenu-reference-et-une-contribution BibNum] [click 'à télécharger' for English analysis]

==External links==

* "Fibonacci, Leonardo, or Leonardo of Pisa." Complete Dictionary of Scientific Biography. 2008. Encyclopedia.com. (April 20, 2015). [http://www.encyclopedia.com/doc/1G2-2830901418.html] *[http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=630&bodyId=1002 Fibonacci] at [https://web.archive.org/web/20060405222111/http://77.1911encyclopedia.org/S/SI/SIMPSON_THOMAS.htm Convergence] * *[http://lhldigital.lindahall.org/cdm/search/collection/math/searchterm/fibonacci/field/creato/mode/all/conn/and/order/nosort Fibonacci (2 vol., 1857 & 1862) Il liber abbaci and Practica Geometriae] - digital facsimile from the Linda Hall Library *[http://www.hs-augsburg.de/~harsch/Chronologia/Lspost13/Fibonacci/fib_intr.html Fibonacci, Liber abbaci] Bibliotheca Augustana

Category:1250 deaths Category:1175 births Category:13th-century Latin writers Category:13th-century Italian mathematicians Category:Fibonacci numbers Category:Italian Roman Catholics Category:Medieval European mathematics Category:Number theorists Category:People from Pisa

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