Fibonacci

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Leonardo of Pisa or Leonardo Pisano (Pisa, c. 1170 - Pisa, 1250), also known as Fibonacci, was an Italian mathematician. He is best known for the discovery of the Fibonacci numbers, and for his role in the introduction to Europe of the modern Arabic positional decimal system for writing and manipulating numbers (algorism).

1 Biography
2 Liber Abaci
3 Important publications
4 References
5 See also
6 External links

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Biography

Leonardo's father Guglielmo (William) was nicknamed Bonacci ('good natured' or 'simple'). Leonardo was posthumously given the nickname Fibonacci (for filius Bonacci, son of Bonacci). William directed a trading post (by some accounts he was the consul for Pisa) in Bugia, a port east of Algiers in the Almohad dynasty's sultanate in barbaresque North Africa (now Bejaia, Algeria), and as a young boy Leonardo traveled there to help him. This is where he learned about the Arabic numeral system.

Perceiving that arithmetic with Arabic numerals (see that article) 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, returning around 1200. In 1202, at age 32, he published what he had learned in Liber Abaci, or Book of Calculation.

Leonardo became a guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honoured Leonardo, under his alternative name of Leonardo Bigollo (meaning good-for-nothing or traveller), by granting him a salary.

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Liber Abaci

In the Liber Abaci, Fibonacci says the following introducing the so called "Modus Indorum" or the method of the Indians, today known as arithmetic and algebra.

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. — (Ref. Sigler, 2003 and Grimm 1973 see references)

In this book he showed the practical importance of the new number system by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interests, money-changing, and numerous other applications. The book was well received throughout educated Europe and had a profound impact on European thought, although the use of decimal numerals did not become widespread until the invention of printing almost three centuries later. (See, for example, the 1482 Ptolemaeus map of the world printed by Lienhart Holle in Ulm.)

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Important publications

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