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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]
Biography
Leonardo was born in Pisa, Italy. 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 western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli.[6]
Important publications
Liber Abaci
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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.
In popular culture
Image:Fibonacci.JPG
Chimney of Turku Energia, Turku, Finland featuring Fibonacci sequence in 2m high neon lights. By Italian artist Mario Merz for an environmental art project (1994)
- 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 in The DaVinci Code and The Da Vinci Code (film).
- 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
- 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.
- The Fibonnaci Sequence, as the God's Equation, is seen in the episode of the same name in Taken.
- The Fibonacci Sequence (Fibonacci Retracement, Fibonacci Fan, Fibonacci Time Zone, and Fibonacci Arc) were often used by global traders (Forex, Stock, Commodities) as the most powerful indicator for predicting movement of the market prices. The Fibonacci sequence of numbers follows a logic that the next number is the sum of the previous two numbers. Thus the sequence is 1,2,3,5,8,13,21,34,55,89,144,233,etc. A very interesting fact about this sequence is that any number divided by the next number in the sequence tends toward a ratio of about 0.618 (more precisely, the golden ratio) and if divided by the next alternate number tends toward a ratio of about 0.382 as you move upward through the sequence.
- FIB and PHI: The golden Proportion in Musical Form by Charles Madden Connects the Fibonacci series with Music Theory.
References
- ^ Howard Eves. An Introduction to the History of Mathematics. Brooks Cole, 1990: ISBN 0-03-029558-0 (6th ed.), p 261.
- ^ Leonardo Pisano - page 3: "Contributions to number theory". Encyclopædia Britannica Online, 2006. Accessed 18 September 2006.
- ^ Parmanand Singh. "Acharya Hemachandra and the (so called) Fibonacci Numbers". Math. Ed. Siwan , 20(1):28-30, 1986. ISSN 0047-6269]
- ^ 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"
- ^ 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.
- ^ Fibonacci's Statue in Pisa
Bibliography
- 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.
See also
External links
- 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 Mathematics archive. University of St Andrews website, Scotland, 1998.
- Liber Abaci and its Egyptian fraction methodsar:ليوناردو فيبوناتشي
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