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'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]

★ The spreading of Hindu-Arabic numeral system in Europe, primarily through the publication in the early 13th century of his ''Book of Calculation'', the ''Liber Abaci''.

★ The Liber Abaci continued the use of Egyptian fraction arithmetic, as copied from Arab sources, as noted by seven conversion methods. Five of the rational number conversion methods date to the Egyptian Middle Kingdom as used in the Egyptian Mathematical Leather Roll, and the Rhind Mathematical Papyrus 2/nth table, and its 84 problems.

★ 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''.^[3]

Contents

Biography

''Liber Abaci''

References

Bibliography

See also

External links

Biography

Leonardo was born in Pisa. 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 barbaresque 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 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.

''Liber Abaci''

Main articles: Liber Abaci

In his work, Fibonacci introduces the so-called ''Modus Indorum'' (method of the Indians), today known as Arabic numerals, as follows (Sigler 2003; Grimm 1973):B C A GH and F.

After my father's appointment by his homeland as state official in the customs house of Bugia for the Pisan merchants who thronged to it, he took charge; and in view of its future usefulness and convenience, had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days.


There, following my introduction, as a consequence of marvelous instruction in the art, to the nine digits of the Hindus, the knowledge of the art very much appealed to me before all others, and for it I realized that all its aspects were studied in Egypt, Syria, Greece, Sicily, and Provence, with their varying methods; and at these places thereafter, while on business.


I pursued my study in depth and learned the give-and-take of disputation. But all this even, and the algorism, as well as the art of Pythagoras, I considered as almost a mistake in respect to the method of the Hindus. (Modus Indorum). Therefore, embracing more stringently that method of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of Euclid's geometric art, I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters.


Almost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its pre-eminent method, might be instructed, and further, in order that the Latin people might not be discovered to be without it, as they have been up to now. If I have perchance omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is blameless and utterly provident in all things.


The nine Indian figures are:

9 8 7 6 5 4 3 2 1


With these nine figures, and with the sign 0 ... any number may be written.

Thus, ''Liber Abaci'' 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. Nevertheless, the use of decimal numerals did not become widespread until the invention of printing almost three centuries later, in 1585 (see, e.g., Ptolemy's world map printed in 1482 by Lienhart Holle in Ulm).
''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.

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.

See also

★ Brahmagupta-Fibonacci identity

★ Cassini and Catalan identities

★ Engel expansion

★ Fibonacci heap

External links

★ Goetzmann, William N., ''Fibonacci and the Financial Revolution'' (October 23, 2003),Yale School of Management International Center for Finance Working Paper No. 03-28 [1]

★ Fibonacci at Convergence

★ Fibonacci @ WikiSource

★ O'Connor, John J and Robertson, Edmund F. "Leonardo Pisano Fibonacci – 1170 - 1250" in ''The MacTutor History of Mathematics archive''. University of St Andrews website, Scotland, 1998.