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Fibonacci
Fibonacci
Leonardo of Pisa (Fibonacci)
Leonardo of Pisa, "Fibonacci" Born Died Residence Nationality Fields Known for c. 1170 Pisa, Italy c. 1250 Pisa, Italy Italy Italian Mathematician Fibonacci number Fibonacci prime Brahmagupta-Fibonacci identity Fibonacci polynomials Fibonacci pseudoprime Fibonacci word Reciprocal Fibonacci constant Introduction of digital notation to Europe Pisano period Practical number Catholic
Statue of Fibonacci. Camposanto, Pisa. 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 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]
Religious stance
Leonardo of Pisa (c. 1170 – c. 1250), also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most
Biography
Leonardo was born in Pisa, Italy in about 1170 to 1250. His father Guglielmo was
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nicknamed Bonacio ("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 to the Middle East where he learned Hindu Arabic numerals. This is where he learned about the Hindu-Arabic numeral system. Recognizing that arithmetic with HinduArabic 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 honored 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 western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli.[6]
Fibonacci
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 sequence
In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers, starting with 0 and 1. Thus the sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 etc. The higher up in the sequence, the closer two consecutive "Fibonacci numbers" of the sequence divided by each other will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1). The golden ratio was used widely in the Renaissance in paintings.
In popular culture
See also: Fibonacci numbers in popular culture • 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 Da Vinci 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
In the Liber Abaci (1202), Fibonacci introduces the so-called modus Indorum (method of the Indians), today known as 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. Liber Abaci also posed, and solved, a problem involving the growth of a hypothetical population of rabbits based on idealized
Books written by Fibonacci
• 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.
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• Di minor guisa (on commercial arithmetic; lost) • Commentary on Book X of Euclid’s Elements (lost)
Fibonacci
[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 "traveler" (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
See also
• • • • • • • • • • • • • • • • • • • • • • • • • Acharya Hemachandra Brahmagupta–Fibonacci identity Carmichael’s theorem Casey Mongoven Egyptian fraction Elliott wave principle Engel expansion Fibonacci coding 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 Verner Emil Hoggatt, Jr. Virahanka Viswanath’s constant Zeckendorf’s theorem
References
• 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.
Notes
[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"
External links
• 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 [1] • 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
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Mathematics archive. University of St Andrews website, Scotland, 1998. • Liber Abaci and its Egyptian fraction methods Persondata NAME Leonardo of Pisa ALTERNATIVE Fibonacci;Pisano, NAMES Leonardo; Bonacci, Leonardo; Fibonacci, Leonardo SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH c. 1170 Pisa, Italy c. 1250 Pisa, Italy
Fibonacci
Retrieved from "http://en.wikipedia.org/wiki/Fibonacci" Categories: 12th-century births, 1250 deaths, People from Pisa, People from Tuscany, 13thcentury Latin writers, 13th-century mathematicians, Fibonacci numbers, Italian mathematicians, Number theorists, Italian Roman Catholics This page was last modified on 18 May 2009, at 13:28 (UTC). All text is available under the terms of the GNU Free Documentation License. (See Copyrights for details.) Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a U.S. registered 501(c)(3) taxdeductible nonprofit charity. Privacy policy About Wikipedia Disclaimers
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