Fibonacci

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Leonardo Bonacci (Template:C. – Template:C.),[1] commonly known as Fibonacci,Template:EfnTemplate:Efn was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".[2]

The name he is commonly called, Fibonacci, is first found in a modern source in a 1838 text by the Franco-Italian mathematician Guglielmo Libri[3][4] and is short for Script error: No such module "Lang". ('son of Bonacci').[5]Template:Efn However, even as early as 1506, Perizolo, a notary of the Holy Roman Empire, mentions him as "Lionardo Fibonacci".[6]

Fibonacci popularized the Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of Script error: No such module "Lang". (Book of Calculation)[7][8] and also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in Script error: No such module "Lang"..[9]

Biography

Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official[10] who directed a trading post in Bugia, modern-day Béjaïa, Algeria.[11] Fibonacci travelled with him as a young boy, and it was in Bugia where he was educated that he learned about the Hindu–Arabic numeral system.[12][1]

Fibonacci travelled around the Mediterranean coast, meeting with many merchants and learning about their systems of doing arithmetic.[13] He soon realised the many advantages of the Hindu-Arabic system, which, unlike the Roman numerals used at the time, allowed easy calculation using a place-value system. In 1202, he completed the Script error: No such module "Lang". (Book of Abacus or The Book of Calculation),[14] which popularized Hindu–Arabic numerals in Europe.[1]

Fibonacci was a guest of Emperor Frederick II, who enjoyed mathematics and science. A member of Frederick II's court, John of Palermo, posed several questions based on Arab mathematical works for Fibonacci to solve. In 1240, the Republic of Pisa honored Fibonacci (referred to as Leonardo Bigollo)[15] 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.[16][17]

Fibonacci is thought to have died between 1240[18] and 1250,[19] in Pisa.

Liber Abaci

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File:Liber abbaci magliab f124r.jpg
A page of Fibonacci's Script error: No such module "Lang". from the Biblioteca Nazionale di Firenze showing (in box on right) the Fibonacci sequence with the position in the sequence labeled with Latin numbers and Roman numerals and the value in Hindu-Arabic numerals

In the Script error: No such module "Lang". (1202), Fibonacci introduced the so-called modus Indorum (method of the Indians), today known as the Hindu–Arabic numeral system,[20][21] with ten digits including a zero and positional notation. The book showed the practical use and value of this 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. Replacing Roman numerals, its ancient Egyptian multiplication method, and using an abacus for calculations, was an advance in making business calculations easier and faster, which assisted the growth of banking and accounting in Europe.[22][23]

The original 1202 manuscript is not known to exist.[24] In a 1228 copy of the manuscript, the first section introduces the numeral system and compares it with others, such as Roman numerals, and methods to convert numbers to it. The second section explains uses 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.[24][22][23]

Fibonacci sequence

Script error: No such module "Labelled list hatnote". Script error: No such module "Lang". posed and solved a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. Although Fibonacci's Script error: No such module "Lang". contains the earliest known description of the sequence outside of India, the sequence had been described by Indian mathematicians as early as the sixth century.[25][26][27][28]

In the Fibonacci sequence, each number is the sum of the previous two numbers. Fibonacci omitted the "0" and first "1" included today and began the sequence with 1, 2, 3, ... . He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next place, the value 377.[29][30] 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 set in Pisa. Today it is located in the western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli.[31][32]

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

See also

Notes

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References

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Further reading

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  • Goetzmann, William N. and Rouwenhorst, K.Geert (2005). The Origins of Value: The Financial Innovations That Created Modern Capital Markets. Oxford University Press Inc., US, Template:Isbn.
  • Goetzmann, William N., Fibonacci and the Financial Revolution (October 23, 2003), Yale School of Management International Center for Finance Working Paper No. 03–28
  • Grimm, R. E., "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 Script error: No such module "Lang". online and analyzed on BibNum [click 'à télécharger' for English analysis]

External links

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  1. ↑ a b c Script error: No such module "citation/CS1".
  2. ↑ Eves, Howard. An Introduction to the History of Mathematics. Brooks Cole, 1990: Template:ISBN (6th ed.), p. 261.
  3. ↑ Script error: No such module "citation/CS1".
  4. ↑ Script error: No such module "citation/CS1".
  5. ↑ Keith Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution, A&C Black, 2012 p. 13.
  6. ↑ Script error: No such module "citation/CS1".
  7. ↑ Script error: No such module "citation/CS1".
  8. ↑ Leonardo Pisano: "Contributions to number theory" Template:Webarchive. Encyclopædia Britannica Online, 2006. p. 3. Retrieved 18 September 2006.
  9. ↑ Singh, Parmanand. "Acharya Hemachandra and the (so called) Fibonacci Numbers". Math. Ed. Siwan, 20(1):28–30, 1986. Template:Catalog lookup linkScript error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".
  10. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named livio
  11. ↑ G. Germano, New editorial perspectives in Fibonacci's Liber abaci, «Reti medievali rivista» 14, 2, pp. 157–173 Template:Webarchive.
  12. ↑ Script error: No such module "citation/CS1".
  13. ↑ In the Prologus of the Liber abacci he said: "Having been introduced there to this art with an amazing method of teaching by means of the nine figures of the Indians, I loved the knowledge of such an art to such an extent above all other arts and so much did I devote myself to it with my intellect, that I learned with very earnest application and through the technique of contradiction anything to be studied concerning it and its various methods used in Egypt, in Syria, in Greece, in Sicily, and in Provence, places I have later visited for the purpose of commerce" (translated by G. Germano, New editorial perspectives in Fibonacci's Liber abaci, «Reti medievali rivista» 14, 2, pp. 157–173 Template:Webarchive.
  14. ↑ The English edition of the Liber abacci was published by L.E. Sigler, Leonardo Pisano's book of calculation, New York, Springer-Verlag, 2003
  15. ↑ 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 "bilingual" or "traveller". A. F. Horadam contends a connotation of "bigollo" is "absent-minded" (see first footnote of "Eight hundred years young" Template:Webarchive), 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.
  16. ↑ Script error: No such module "citation/CS1".
  17. ↑ «Considerantes nostre civitatis et civium honorem atque profectum, qui eis, tam per doctrinam quam per sedula obsequia discreti et sapientis viri magistri Leonardi Bigolli, in abbacandis estimationibus et rationibus civitatis eiusque officialium et aliis quoties expedit, conferuntur; ut eidem Leonardo, merito dilectionis et gratie, atque scientie sue prerogativa, in recompensationem laboris sui quem substinet in audiendis et consolidandis estimationibus et rationibus supradictis, a Comuni et camerariis publicis, de Comuni et pro Comuni, mercede sive salario suo, annis singulis, libre xx denariorum et amisceria consueta dari debeant (ipseque pisano Comuni et eius officialibus in abbacatione de cetero more solito serviat), presenti constitutione firmamus». F. Bonaini, Memoria unica sincrona di Leonardo Fibonacci, novamente scoperta, «Giornale storico degli archivi toscani» 1, 4, 1857, pp. 239–246.
  18. ↑ Script error: No such module "citation/CS1"..
  19. ↑ Script error: No such module "citation/CS1"..
  20. ↑ a b Script error: No such module "citation/CS1".
  21. ↑ Grimm 1973
  22. ↑ a b Script error: No such module "citation/CS1".
  23. ↑ a b Script error: No such module "citation/CS1".
  24. ↑ a b Script error: No such module "citation/CS1".
  25. ↑ Script error: No such module "Citation/CS1".
  26. ↑ Script error: No such module "citation/CS1".
  27. ↑ Script error: No such module "citation/CS1".
  28. ↑ Hall, Rachel W. Math for poets and drummers Template:Webarchive. Math Horizons 15 (2008) 10–11.
  29. ↑ Template:Cite OEIS
  30. ↑ Script error: No such module "citation/CS1".
  31. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named statue
  32. ↑ Script error: No such module "citation/CS1".
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