Fibonacci

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Fibonacci

Fibonacci, Leonardo, b. c.1170, d. after 1240, Italian mathematician, known also as Leonardo da Pisa. In Liber abaci (1202, 2d ed. 1228), for centuries a standard work on algebra and arithmetic, he advocated the adoption of Arabic notation. In Practica geometriae (1220) he organized and extended the material then known in geometry and trigonometry. The sequence of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, … , formed by adding consecutive members, is named for him; it occurs in higher mathematics in various connections. Baldassare Boncompagni edited his works (2 vol., 1857-62).

The Columbia Electronic Encyclopedia Copyright © 2004.
Licensed from Columbia University Press

Fibonacci

Leonardo of Pisa (c. 1170 – c. 1250), also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented mathematician of the Middle Ages".

Fibonacci is best known to the modern world for:

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.
A modern number sequence named after him known as the Fibonacci numbers, which he did not discover but used as an example in the Liber Abaci.

Biography

Leonardo was born in Pisa, Italy in c. 1170 (The exact date of birth is unknown). His father Guglielmo was nicknamed Bonaccio ("good natured" or "simple"). Leonardo's mother, Alessandra, died when he was nine years old. Leonardo was posthumously given the nickname Fibonacci (derived from filius Bonacci, meaning son of Bonaccio).

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 there to help him. This is where he learned about the Hindu-Arabic numeral system.

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 honoured Leonardo, referred to as Leonardo Bigollo, 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.

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 hypothetical 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

In the Fibonacci sequence of numbers, each number after the first two, is the sum of the previous two numbers. Thus the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc.

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

In popular culture

Fibonacci's name was adopted by a Los Angeles-based art rock group, The Fibonaccis, that recorded from 1982-1987.
Fibonacci and the Fibonacci numbers are mentioned as a code to unlock a vessel in Dan Brown's best selling novel, The DaVinci Code, and its movie adaptation.
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.

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 Fibonacci's identity.
Di minor guisa (on commercial arithmetic; lost)
Commentary on Book X of Euclid's Elements (lost)

References

Bibliography

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.