The Info List - Fibonacci

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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" (Italian: ), 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_.


* 1 History * 2 _Liber Abaci_ (1202) * 3 Fibonacci sequence * 4 Legacy * 5 Works * 6 See also * 7 References * 8 Further reading * 9 External links


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 .

Fibonacci travelled extensively around the Mediterranean coast, meeting with many merchants and learning about their systems of doing arithmetic. He soon realised the many advantages of the Hindu-Arabic system. In 1202, he completed the _ Liber Abaci _ (_Book of Abacus_ or _Book of Calculation_) which popularized Hindu–Arabic numerals in Europe.

Fibonacci became a guest of Emperor Frederick II , who enjoyed mathematics and science. In 1240, the Republic of Pisa honored Fibonacci (referred to as Leonardo Bigollo) 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)

_ A page of Fibonacci's Liber Abaci _ from the Biblioteca Nazionale di Firenze showing (in box on right) the Fibonacci sequence with the position in the sequence labeled in Roman numerals and the value in Hindu-Arabic numerals. Main article: Liber Abaci

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 1228 edition, first section introduces the Arabic numeral system and compares the system with other systems, such as Roman numerals, and methods to convert the other numeral systems into Arabic numerals. Replacing the Roman numeral system, its ancient Egyptian multiplication method, and using an abacus for calculations, with an Arabic numeral system was an advance in making business calculations easier and faster, which led to the growth of banking and accounting in Europe.

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 .


Main article: Fibonacci number

_Liber Abaci_ 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 _Liber Abaci_ contains the earliest known description of the sequence outside of India, the sequence had been noted by Indian mathematicians as early as the sixth century.

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.


Monument of Leonardo da Pisa (Fibonacci), by Giovanni Paganucci, completed in 1863, in the Camposanto di Pisa .

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 .


* _ 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)


* Fibonacci numbers in popular culture * Republic of Pisa


* ^ Smith, David Eugene; Karpinski, Louis Charles (1911), _The Hindu-Arabic Numerals_, Boston and London: Ginn and Company, p. 128 . * ^ _A_ _B_ _C_ Knott, R. "Who was Fibonacci?". Maths.surrey.ac.uk. Retrieved 2010-08-02. * ^ Eves, Howard . _An Introduction to the History of Mathematics_. Brooks Cole, 1990: ISBN 0-03-029558-0 (6th ed.), p 261. * ^ "Fibonacci." _Collins English Dictionary – Complete and Unabridged, 12th Edition 2014_. 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014. HarperCollins Publishers 23 Jun. 2017 http://www.thefreedictionary.com/Fibonacci * ^ Kieth Devllin "Finding Fibonacci" Princeton Univertsity Press 2017 pg 24 * ^ Keith Devlin , _The Man of Numbers: Fibonacci's Arithmetic Revolution,_A&C Black, 2012 p.13. * ^ " Fibonacci Numbers". _www.halexandria.org_. * ^ Leonardo Pisano – page 3: "Contributions to number theory". Encyclopædia Britannica Online, 2006. Retrieved 18 September 2006. * ^ Singh, Parmanand. "Acharya Hemachandra and the (so called) Fibonacci Numbers". _Math_. Ed. Siwan , 20(1):28–30, 1986. ISSN 0047-6269 ]

* ^ 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. * ^ Keith Devlin (7 November 2002). "A man to count on". The Guardian. Retrieved 7 June 2016. * ^ Koshy, Thomas (2011), _ Fibonacci and Lucas Numbers with Applications_, John Wiley & Sons, p. 3, ISBN 9781118031315 . * ^ Tanton, James Stuart (2005), _Encyclopédia of Mathematics_, Infobase Publishing, p. 192, ISBN 9780816051243 . * ^ _A_ _B_ Sigler, Laurence E. (trans.) (2002), _Fibonacci's Liber Abaci_, Springer-Verlag, ISBN 0-387-95419-8 * ^ Grimm 1973 * ^ _A_ _B_ Gordon, John Steele . "The Man Behind Modern Math". Retrieved 2015-08-28. * ^ _A_ _B_ "Fibonacci: The Man Behind The Math". _NPR.org_. Retrieved 2015-08-29. * ^ _A_ _B_ Devlin, Keith. "The Man of Numbers: Fibonacci\'s Arithmetic Revolution ". Retrieved 2015-08-29. * ^ Singh, Pamanand (1985). "The so-called fibonacci numbers in ancient and medieval India". _Historia Mathematica_. 12: 229–244. doi :10.1016/0315-0860(85)90021-7 . * ^ Goonatilake, Susantha (1998). _Toward a Global Science_. Indiana University Press. p. 126. ISBN 978-0-253-33388-9 . * ^ Knuth, Donald (2006). _The Art of Computer Programming: Generating All Trees – History of Combinatorial Generation; Volume 4_. Addison-Wesley. p. 50. ISBN 978-0-321-33570-8 . * ^ Hall, Rachel W. Math for poets and drummers. _Math Horizons_ 15 (2008) 10–11. * ^ Fibonacci Numbers from The On-Line Encyclopedia of Integer Sequences. * ^ Pisanus, Leonardus; Boncompagni, Baldassarre (1 January 1857). _Scritti: Il Liber Abbaci_. Tip. delle Scienze Fisiche e Matematiche. p. 231 – via Google Books. * ^ "Fibonacci\'s Statue in Pisa". Epsilones.com. Retrieved 2010-08-02.


* Devlin, Keith (2012). _The Man of Numbers: Fibonacci's Arithmetic Revolution_. Walker Books. ISBN 978-0802779083 . * 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 0-19-517571-9 . * 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 _Liber Abaci_ online and analyzed on _BibNum_


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