Fibonacci

For the number sequence, see Fibonacci number. For the Prison Break character, see Otto Fibonacci.
Leonardo of Pisa (Fibonacci)
Leonardo of Pisa, "Fibonacci"
Leonardo of Pisa, "Fibonacci"
Born c. 1180
Pisa, Italy
Died c. 1250
Pisa, Italy
Residence Italy
Nationality Italian
Fields Mathematician
Known for Fibonacci number
Fibonacci prime
Brahmagupta-Fibonacci identity
Fibonacci polynomials
Fibonacci pseudoprime
Fibonacci word
Reciprocal Fibonacci constant
Fibonacci family
Introduction of digital notation to Europe
Pisano period
Practical number
Religious stance Catholic
Statue of Fibonacci. Camposanto, Pisa.

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".[1]

Fibonacci is best known to the modern world for:[2]

Contents

Biography

Leonardo was born in Pisa, Italy in about 1170. 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).[4]

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,[5] 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.[6]

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 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

Main article: Fibonacci number

In the Fibonacci sequence of numbers, each number (after the first two) is the sum of the previous two numbers. Thus the sequence begins 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

See also: Fibonacci numbers in popular culture

Books written by Fibonacci

See also

References

  1. ↑ Howard Eves. An Introduction to the History of Mathematics. Brooks Cole, 1990: ISBN 0-03-029558-0 (6th ed.), p 261.
  2. ↑ Leonardo Pisano - page 3: "Contributions to number theory". Encyclopædia Britannica Online, 2006. Accessed 18 September 2006.
  3. ↑ Parmanand Singh. "Acharya Hemachandra and the (so called) Fibonacci Numbers". Math. Ed. Siwan , 20(1):28-30, 1986. ISSN 0047-6269]
  4. ↑ See the incipit of the Liber Abaci: "Incipit liber Abaci Compositus a leonardo filio Bonacij Pisano" (copied from the "Prologus" of the Liber Ab(b)aci at Latin Wikisource - emphasis added), in English: "Here starts the book of Calculation Written by Leonardo son of Bonaccio, from Pisa"
  5. ↑ 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.
  6. ↑ Fibonacci's Statue in Pisa

Bibliography

External links

Persondata
NAME Leonardo of Pisa
ALTERNATIVE NAMES Fibonacci;Pisano, Leonardo; Bonacci, Leonardo; Fibonacci, Leonardo
SHORT DESCRIPTION
DATE OF BIRTH c. 1170
PLACE OF BIRTH Pisa, Italy
DATE OF DEATH c. 1250
PLACE OF DEATH Pisa, Italy