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Fibonacci | |
---|---|

Portrait by unknown artist | |

Born | c. 1170-75 in Pisa^{[1]} |

Died | c. 1240 (aged around 70) Most likely Pisa |

Nationality | Italian |

Known for | The Liber Abaci Fibonacci number The introduction of digital notation to Europe |

Religion | Catholic |

Parents | Guglielmo Bonacci |

For the number sequence, see Fibonacci number. For the Prison Break character, see Otto Fibonacci.

Fibonacci | |
---|---|

Portrait by unknown artist | |

Born | c. 1170-75 in Pisa^{[1]} |

Died | c. 1240 (aged around 70) Most likely Pisa |

Nationality | Italian |

Known for | The Liber Abaci Fibonacci number The introduction of digital notation to Europe |

Religion | Catholic |

Parents | Guglielmo Bonacci |

**Leonardo Bonacci** (c. 1170 – c. 1250)^{[2]}—known as **Fibonacci** (Italian: [fiboˈnattʃi]), and also **Leonardo of Pisa**, **Leonardo Pisano**, **Leonardo Pisano Bigollo**, **Leonardo Fibonacci**—was an Italian mathematician, considered by some "the most talented Western mathematician of the Middle Ages."^{[3]}

Fibonacci is best known to the modern world for^{[4]} the spreading of the Hindu–Arabic numeral system in Europe, primarily through his composition in 1202 of *Liber Abaci* (*Book of Calculation*), and for a number sequence named the Fibonacci numbers after him, which he did not discover but used as an example in the *Liber Abaci*.^{[5]}

Fibonacci was born around 1170 to Guglielmo Bonacci, 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 traveled with him as a young boy, and it was in Bugia (now Béjaïa, Algeria) that he learned about the Hindu–Arabic numeral system.^{[2]}

Alternatively, according to a history text by mathematician Tobias Dantzig, his father was "a lowly shipping clerk nicknamed Bonaccio, which, in the idiom of the period, meant 'simpleton' ... hence 'Fibonacci,' the 'son of a simpleton.'"^{[6]} But this hardly accords with Fibonacci's own description of his father, in the introduction to *Liber Abaci*, as 'a public official ... in the Bugia customshouse established for the Pisan merchants'.^{[7]}

Recognizing that arithmetic with Hindu–Arabic numerals is simpler and more efficient than with Roman numerals, Fibonacci travelled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. He returned from his travels in around 1200, and in 1202, the 32-year-old recorded what he had learned in *Liber Abaci* (*Book of Abacus* or *Book of Calculation*), and thereby 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)^{[8]} by granting him a salary.

The date of Fibonacci's death is not known, but it has been estimated to be between 1240^{[9]} and 1250,^{[10]} most likely in Pisa.

Main article: Liber Abaci

In the *Liber Abaci* (1202), Fibonacci introduced the so-called *modus Indorum* (method of the Indians), today known as 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 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.

Main article: Fibonacci number

*Liber Abaci* also 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. The number sequence was known to Indian mathematicians as early as the 6th century,^{[11]}^{[12]}^{[13]} but it was Fibonacci's *Liber Abaci* that introduced it to the West.

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.^{[14]}^{[15]} 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 constructed and erected in Pisa. Today it is located in the western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli.^{[16]}

There are many mathematical concepts named after Fibonacci, for instance 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, Springer, 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 the Brahmagupta–Fibonacci identity.*Di minor guisa*(on commercial arithmetic; lost)*Commentary on Book X of Euclid's Elements*(lost)

**^***The Hindu-Arabic Numerals*. David Eugene Smith and Louis Charles Karpinski, 1911: p.128- ^
^{a}^{b}Dr R Knott. "Who was Fibonacci?". Maths.surrey.ac.uk. Retrieved 2010-08-02. **^**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. Retrieved 18 September 2006.**^**Parmanand Singh. "Acharya Hemachandra and the (so called) Fibonacci Numbers".*Math*. Ed. Siwan , 20(1):28–30, 1986. ISSN 0047-6269]**^**Dantzig, Tobias (1983),*Mathematics in Ancient Greece*, Dover Publications,Inc., p. 113, ISBN 0-486-45347-2.**^***Liber Abaci*, English translation by L E Sigler, 2002**^**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.**^**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.**^**Susantha Goonatilake (1998).*Toward a Global Science*. Indiana University Press. p. 126. ISBN 978-0-253-33388-9.**^**Donald Knuth (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.**^**Rachel W. Hall. Math for poets and drummers.*Math Horizons***15**(2008) 10–11.**^**Fibonacci Numbers from The On-Line Encyclopedia of Integer Sequences.**^***Il Liber Abbaci*, 1857 edition, p. 231. Online at**^**"Fibonacci's Statue in Pisa". Epsilones.com. Retrieved 2010-08-02.

- 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. - 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.

- Goetzmann, William N.,
*Fibonacci and the Financial Revolution*(October 23, 2003), Yale School of Management International Center for Finance Working Paper No. 03–28 - Fibonacci at Convergence
- O'Connor, John J.; Robertson, Edmund F., "Leonardo Pisano Fibonacci",
*MacTutor History of Mathematics archive*, University of St Andrews.