Fibonacci

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For the number sequence, see Fibonacci number. For the Prison Break character, see Otto Fibonacci.
Fibonacci
Fibonacci.jpg
Portrait by unknown artist
Born C. 1170
Died C. 1250 (aged around 80)
Nationality Italian
Known for Fibonacci number
Fibonacci prime
Brahmagupta–Fibonacci identity
Fibonacci polynomials
Fibonacci pseudoprime
Fibonacci word
Reciprocal Fibonacci constant
Introduction of digital notation to Europe
Pisano period
Practical number
Religion Catholic
Parents Guglielmo Bonacci

Leonardo Pisano Bigollo (c. 1170 – c. 1250)[1] – known as Fibonacci, and also Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci – was an Italian mathematician, considered by some "the most talented western mathematician of the Middle Ages."[2]

Fibonacci is best known to the modern world for[3] the spreading of the Hindu–Arabic numeral system in Europe, primarily through the publication in 1202 of his 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.[4]

Contents

Life [edit]

Leonardo Fibonacci was born around 1170 to Guglielmo Bonacci, he was a wealthy Italian merchant. Guglielmo directed a trading post (by some accounts he was the consultant for Pisa) in Bugia, a port east of Algiers in the Almohad dynasty's sultanate in North Africa (now Béjaïa, Algeria). As a young boy, Leonardo traveled with him to help; it was there he learned about the Hindu–Arabic numeral system. [5]

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. Leonardo returned from his travels around 1200. In 1202, at the age of 32, he published what he had learned in Liber Abaci (Book of Abacus or Book of Calculation), and thereby popularized Hindu–Arabic numerals in Europe.

Leonardo became an amicable guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honored Leonardo, referred to as Leonardo Bigollo,[6] by granting him a salary.

Fibonacci died in Pisa, but the date of his death is unknown, with estimates ranging from 1240[7] to 1250.[8]

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.[9]

Liber Abaci [edit]

Main article: Liber Abaci

In the Liber Abaci (1202), Fibonacci introduces 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, using lattice multiplication and Egyptian fractions, 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.

Fibonacci sequence [edit]

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,[10][11][12] 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, starting with 0 and 1. This sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ... [13]

The higher up in the sequence, the more closely the ratio of two consecutive Fibonacci numbers will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1).

19th century statue of Fibonacci in Camposanto, Pisa.

See also [edit]

Notes [edit]

  1. ^ "The Fibonacci Series - Biographies - Leonardo Fibonacci (ca.1175 - ca.1240)". Library.thinkquest.org. Retrieved 2010-08-02. 
  2. ^ Howard Eves. An Introduction to the History of Mathematics. Brooks Cole, 1990: ISBN 0-03-029558-0 (6th ed.), p 261.
  3. ^ Leonardo Pisano - page 3: "Contributions to number theory". Encyclopædia Britannica Online, 2006. Retrieved 18 September 2006.
  4. ^ Parmanand Singh. "Acharya Hemachandra and the (so called) Fibonacci Numbers". Math. Ed. Siwan , 20(1):28-30, 1986. ISSN 0047-6269]
  5. ^ Dr R Knott: fibandphi (AT) ronknott DOT com. "Who was Fibonacci?". Maths.surrey.ac.uk. Retrieved 2010-08-02. 
  6. ^ 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.
  7. ^ Koshy, Thomas (2011), Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, p. 3, ISBN 9781118031315 .
  8. ^ Tanton, James Stuart (2005), Encyclopédia of Mathematics, Infobase Publishing, p. 192, ISBN 9780816051243 .
  9. ^ "Fibonacci's Statue in Pisa". Epsilones.com. Retrieved 2010-08-02. 
  10. ^ Susantha Goonatilake (1998). Toward a Global Science. Indiana University Press. p. 126. ISBN 978-0-253-33388-9. 
  11. ^ 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. 
  12. ^ Rachel W. Hall. Math for poets and drummers. Math Horizons 15 (2008) 10-11.
  13. ^ Fibonacci Numbers from The On-Line Encyclopedia of Integer Sequences.

References [edit]

  • 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.

External links [edit]

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