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# Fibonacci

Leonardo Pisano Bogollo (c. 1170 – c. 1250)[1] also known as Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply 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 the early 13th century of his Book of Calculation, the Liber Abaci; and for a number sequence named after him known as the Fibonacci numbers, which he did not discover but used as an example in the Liber Abaci.[4]

Life

Leonardo Fibonacci was born around 1170 to Guglielmo Fibonacci, 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 Bejaia, 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 traveled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. Leonardo returned from his travels around 1200. In 1202, at age 32, he published what he had learned in Liber Abaci (Book of Abacus or Book of Calculation), and thereby introduced Hindu-Arabic numerals to 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.

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.[7]

Liber Abaci

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.

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, but it was Fibonacci's Liber Abaci that introduced it to the West.

Fibonacci sequence

Main article: Fibonacci number

In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers, starting with 0 and 1. Thus the sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 etc.

The higher up in the sequence, the closer two consecutive "Fibonacci numbers" of the sequence divided by each other will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1).

The golden ratio was used widely in the Renaissance in paintings.

In popular culture

See also: Fibonacci numbers in popular culture

* Fibonacci's name was adopted by a Los Angeles-based art rock group, The Fibonaccis, that recorded from 1981 to 1987.

* Stock traders frequently look to the "Fibonacci retracement" when predicting future share prices.

* A youthful Fibonacci is one of the main characters in the novel Crusade in Jeans (1973). He was left out of the 2006 movie version, however.

* In The Da Vinci Code, the Fibonacci sequence was used as a code but also confused the characters.

19th century statue of Fibonacci in Camposanto, Pisa.

Books written by Fibonacci

* Liber Abaci (1202), a book on calculations (English translation by Laurence Sigler, Springer, 2002)

* Practica Geometriae (1220), a compendium on geometry and trigonometry.

* 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)

See also

* List of topics named after Fibonacci

* Brahmagupta–Fibonacci identity

* Elliott wave principle

* Engel expansion

* Fibonacci search technique

* Golden ratio

* Hylomorphism (computer science)

* Pisano period

* Practical number

* Primefree sequence

* Verner Emil Hoggatt, Jr.

Notes

1. ^ "The Fibonacci Series - Biographies - Leonardo Fibonacci (ca.1175 - ca.1240)". Library.thinkquest.org. http://library.thinkquest.org/27890/biographies1.html. 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. http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html. 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 "traveler" (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. ^ "Fibonacci's Statue in Pisa". Epsilones.com. http://www.epsilones.com/documentos/d-fibonacci.html#fibonacci-ingles. Retrieved 2010-08-02.

References

* 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 0195175719.

* 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

* Fibonacci Biography

* Who was Fibonacci? by Ron Knott.

* 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, http://www-history.mcs.st-andrews.ac.uk/Biographies/Fibonacci.html .

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