Statue of Fibonacci (1863) by Giovanni Paganucci in the Camposanto di Pisa[a]
Bornc. 1170
Diedc. 1250(1250-00-00) (aged 79–80)
Pisa, Republic of Pisa
Other names
  • Leonardo Fibonacci
  • Leonardo Bonacci
  • Leonardo Pisano
Known for
ParentGuglielmo "Bonacci" (father)

Fibonacci (/ˌfɪbəˈnɑːi/;[3] also US: /ˌfb-/,[4][5] Italian: [fiboˈnattʃi]; c. 1170c. 1240–50),[6] also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'[7]), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".[8]

The name he is commonly called, Fibonacci, was made up in 1838 by the Franco-Italian historian Guillaume Libri[9][10] and is short for filius Bonacci ('son of Bonacci').[11][b] However, even earlier, in 1506, a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci".[12]

Fibonacci popularized the Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of Liber Abaci (Book of Calculation)[13][14] and also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in Liber Abaci.[15]


Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official.[7] Guglielmo directed a trading post in Bugia (Béjaïa), in modern-day Algeria.[16] Fibonacci travelled with him as a young boy, and it was in Bugia (Algeria) where he was educated that he learned about the Hindu–Arabic numeral system.[17][6]

Fibonacci travelled around the Mediterranean coast, meeting with many merchants and learning about their systems of doing arithmetic.[18] 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 Liber Abaci (Book of Abacus or The Book of Calculation),[19] which popularized Hindu–Arabic numerals in Europe.[6]

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)[20] 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.[21][22]

Fibonacci is thought to have died between 1240[23] and 1250,[24] in Pisa.

Liber Abaci

Main article: Liber Abaci

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 with Latin numbers and Roman numerals and the value in Hindu-Arabic numerals

In the Liber Abaci (1202), Fibonacci introduced the so-called modus Indorum (method of the Indians), today known as the Hindu–Arabic numeral system,[25][26] 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.[27][28]

The original 1202 manuscript is not known to exist.[29] 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.[29][27][28]

Fibonacci sequence

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 described by Indian mathematicians as early as the sixth century.[30][31][32][33]

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.[34][35] Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence.


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.[1][36]

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.


See also


  1. ^ Fibonacci's actual appearance is not known.[1]
  2. ^ The etymology of Bonacci is "good-natured", so the full name means "son from a good-natured [family]".[7]


  1. ^ a b "Fibonacci's Statue in Pisa". Archived from the original on 2014-02-22. Retrieved 2010-08-02.
  2. ^ Smith, David Eugene; Karpinski, Louis Charles (1911), The Hindu–Arabic Numerals, Boston and London: Ginn and Company, p. 128, archived from the original on 2023-03-13, retrieved 2016-03-02.
  3. ^ "Fibonacci, Leonardo". Lexico UK English Dictionary. Oxford University Press. Archived from the original on 2021-05-12.
  4. ^ "Fibonacci series" Archived 2019-06-23 at the Wayback Machine and "Fibonacci sequence". Collins English Dictionary. HarperCollins. Archived from the original on 12 June 2012. Retrieved 23 June 2019.
  5. ^ "Fibonacci number". Dictionary. Retrieved 23 June 2019.
  6. ^ a b c MacTutor, R. "Leonardo Pisano Fibonacci". Archived from the original on 2019-10-28. Retrieved 2018-12-22.
  7. ^ a b c Livio, Mario (2003) [2002]. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number (First trade paperback ed.). New York City: Broadway Books. pp. 92–93. ISBN 0-7679-0816-3. Archived from the original on 2023-03-13. Retrieved 2018-12-19.
  8. ^ Eves, Howard. An Introduction to the History of Mathematics. Brooks Cole, 1990: ISBN 0-03-029558-0 (6th ed.), p. 261.
  9. ^ Devlin, Keith (2017). Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World. Princeton University Press. p. 24.
  10. ^ Colin Pask (7 July 2015). Great Calculations: A Surprising Look Behind 50 Scientific Inquiries. Prometheus Books. p. 35. ISBN 978-1-63388-029-0. Archived from the original on 13 March 2023. Retrieved 19 January 2020.
  11. ^ Keith Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution, A&C Black, 2012 p. 13.
  12. ^ Drozdyuk, Andriy; Drozdyuk, Denys (2010). Fibonacci, his numbers and his rabbits. Toronto: Choven Pub. p. 18. ISBN 978-0-9866300-1-9. OCLC 813281753. Archived from the original on 2020-02-17. Retrieved 2020-01-26.
  13. ^ "Fibonacci Numbers". Archived from the original on 2019-10-13. Retrieved 2015-04-29.
  14. ^ Leonardo Pisano: "Contributions to number theory" Archived 2008-06-17 at the Wayback Machine. Encyclopædia Britannica Online, 2006. p. 3. Retrieved 18 September 2006.
  15. ^ Singh, Parmanand. "Acharya Hemachandra and the (so called) Fibonacci Numbers". Math. Ed. Siwan, 20(1):28–30, 1986. ISSN 0047-6269
  16. ^ G. Germano, New editorial perspectives in Fibonacci's Liber abaci, «Reti medievali rivista» 14, 2, pp. 157–173 Archived 2021-07-09 at the Wayback Machine.
  17. ^ Thomas F. Glick; Steven Livesey; Faith Wallis (2014). Medieval Science, Technology, and Medicine: An Encyclopedia. Routledge. p. 172. ISBN 978-1-135-45932-1. Archived from the original on 2023-03-13. Retrieved 2018-12-07.
  18. ^ 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 Archived 2021-07-09 at the Wayback Machine.
  19. ^ The English edition of the Liber abacci was published by L.E. Sigler, Leonardo Pisano's book of calculation, New York, Springer-Verlag, 2003
  20. ^ 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" Archived 2008-12-19 at the Wayback Machine), 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.
  21. ^ Keith Devlin (7 November 2002). "A man to count on". The Guardian. Archived from the original on 17 September 2016. Retrieved 7 June 2016.
  22. ^ «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.
  23. ^ Koshy, Thomas (2011), Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, p. 3, ISBN 9781118031315, archived from the original on 2023-03-13, retrieved 2015-12-12.
  24. ^ Tanton, James Stuart (2005), Encyclopédia of Mathematics, Infobase Publishing, p. 192, ISBN 9780816051243, archived from the original on 2023-03-13, retrieved 2015-12-12.
  25. ^ a b Fibonacci's Liber Abaci, translated by Sigler, Laurence E., Springer-Verlag, 2002, ISBN 0-387-95419-8
  26. ^ Grimm 1973
  27. ^ a b "Fibonacci: The Man Behind The Math". Archived from the original on 2011-07-16. Retrieved 2015-08-29.
  28. ^ a b Devlin, Keith. "The Man of Numbers: Fibonacci's Arithmetic Revolution [Excerpt]". Scientific American. Archived from the original on 2014-06-18. Retrieved 2015-08-29.
  29. ^ a b Gordon, John Steele. "The Man Behind Modern Math". Archived from the original on 2015-08-23. Retrieved 2015-08-28.
  30. ^ Singh, Pamanand (1985). "The so-called fibonacci numbers in ancient and medieval India". Historia Mathematica. 12 (3): 229–244. doi:10.1016/0315-0860(85)90021-7.
  31. ^ Goonatilake, Susantha (1998). Toward a Global Science. Indiana University Press. p. 126. ISBN 978-0-253-33388-9. Virahanka Fibonacci.
  32. ^ 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. Archived from the original on 2023-03-13. Retrieved 2020-11-11.
  33. ^ Hall, Rachel W. Math for poets and drummers Archived 2012-02-12 at the Wayback Machine. Math Horizons 15 (2008) 10–11.
  34. ^ Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci Numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  35. ^ Pisanus, Leonardus; Boncompagni, Baldassarre (1 January 1857). Scritti: Il Liber Abbaci. Tip. delle Scienze Fisiche e Matematiche. p. 231. Archived from the original on 13 March 2023. Retrieved 20 December 2018 – via Google Books.
  36. ^ Devlin, Keith (2010). "The Man of Numbers: In Search of Leonardo Fibonacci" (PDF). Mathematical Association of America. pp. 21–28. Archived (PDF) from the original on 2015-09-07. Retrieved 2018-12-21.

Further reading