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FIBONACCI (c. 1175 – c. 1250) was an Italian mathematician from the Republic of Pisa
Pisa
, 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
Fibonacci
popularized the Hindu–Arabic numeral system
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
Fibonacci
numbers , which he used as an example in Liber Abaci.

CONTENTS

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

HISTORY

Fibonacci
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
Almohad dynasty
's sultanate in North Africa . Fibonacci
Fibonacci
travelled with him as a young boy, and it was in Bugia (now Béjaïa
Béjaïa
, Algeria
Algeria
) that he learned about the Hindu–Arabic numeral system
Hindu–Arabic numeral system
.

Fibonacci
Fibonacci
travelled extensively around the Mediterranean
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
Liber Abaci
(Book of Abacus
Abacus
or Book of Calculation) which popularized Hindu–Arabic numerals in Europe.

Fibonacci
Fibonacci
became a guest of Emperor Frederick II , who enjoyed mathematics and science. In 1240, the Republic of Pisa
Pisa
honored Fibonacci
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
Liber Abaci
from the Biblioteca Nazionale di Firenze showing (in box on right) the Fibonacci
Fibonacci
sequence with the position in the sequence labeled in Roman numerals and the value in Hindu-Arabic numerals. Main article: Liber Abaci
Liber Abaci

In the Liber Abaci
Liber Abaci
(1202), Fibonacci
Fibonacci
introduced the so-called modus Indorum (method of the Indians), today known as the Hindu–Arabic numeral system . The book advocated numeration with the digits 0–9 and place value . The book showed the practical use and value of the new Hindu-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 Hindu-Arabic numeral system and compares the system with other systems, such as Roman numerals, and methods to convert the other numeral systems into Hindu-Arabic numerals. Replacing the Roman numeral system, its ancient Egyptian multiplication method, and using an abacus for calculations, with a Hindu-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 Hindu-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 .

FIBONACCI SEQUENCE

Main article: Fibonacci number
Fibonacci number

Liber Abaci
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
Fibonacci
numbers . Although Fibonacci's Liber Abaci
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
Fibonacci
sequence of numbers, each number is the sum of the previous two numbers. Fibonacci
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
Fibonacci
did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence.

LEGACY

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

In the 19th century, a statue of Fibonacci
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
Piazza dei Miracoli
.

In 1877, Éduouard Lucas paid tribute to Fibonacci
Fibonacci
by naming the Fibonacci
Fibonacci
Sequence in his honor.

There are many mathematical concepts named after Fibonacci
Fibonacci
because of a connection to the Fibonacci
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
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

* Adelard of Bath
Adelard of Bath
* Fibonacci numbers in popular culture * Republic of Pisa
Pisa

REFERENCES

* ^ Smith, David Eugene; Karpinski, Louis Charles (1911), The Hindu-Arabic Numerals, Boston and London: Ginn and Company, p. 128 . * ^ A B C D E F G H " Fibonacci
Fibonacci
– Medieval Mathematics – The Story of Mathematics". www.storyofmathematics.com. Retrieved 2017-11-18. * ^ 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
Keith Devlin
, The Man of Numbers: Fibonacci's Arithmetic Revolution,A&C Black, 2012 p.13. * ^ " Fibonacci
Fibonacci
Numbers". www.halexandria.org. * ^ Leonardo Pisano – page 3: "Contributions to number theory". Encyclopædia Britannica
Encyclopædia Britannica
Online, 2006. Retrieved 18 September 2006. * ^ Singh, Parmanand. "Acharya Hemachandra and the (so called) Fibonacci
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
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
Keith Devlin
(7 November 2002). "A man to count on". The Guardian. Retrieved 7 June 2016. * ^ Koshy, Thomas (2011), Fibonacci
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
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.

FURTHER READING

* 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
Fibonacci
and the Financial Revolution (October 23, 2003), Yale School of Management
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
Liber Abaci
online and analyzed on BibNum

EXTERNAL LINKS

Wikisource
Wikisource
has the text of

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