This entry contributed by Margherita Barile

Italian mathematician who was the first great Western mathematician after the decline of Greek science. The son of a merchant, Fibonacci drew the motivation to mathematical inquiry from his commercial trips to the the Orient. It was somewhere between Barbary (Maghreb) and Constantinople (now Istanbul) that he got acquainted with the Hindu-Arabic number system and discovered its enormous practical advantages compared to the Roman numerals, which were still current in Western Europe.

Performing even the simplest arithmetical operations with a non-positional notation was a difficult endeavor: for this task the merchants were forced to resort to the abacus, a device where the numbers were represented by moving balls. Fibonacci exposed the new alternate computing method--based on written algorithms rather than on counting objects--in his Liber Abaci, first issued in 1202. The book began with a presentation of what he called the ten "Indian figures" (0, 1, 2, ..., 9). It was intended as an algebra manual for commercial use, and explained the arithmetical rules using numerical examples derived, for example, from measure and currency conversion, which were translated into proportions and solved by multiplication (rule of three). The so-called Fibonacci sequence arose in this book from a concrete question concerning the growth of a rabbit population. Geometric progressions also appeared in problems related to legacy and interest.

The treatise Practica Geometriae, published in 1225, is mainly inspired by Greek mathematics; it contains theorems from Euclid's Elements and also Heron's formula for the area of a triangle.

Fibonacci distinguished himself in the mathematical competitions proposed at the court of Emperor Frederick II of Hohenstaufen, King of the Two Sicilies, who had his royal seat in Palermo. His striking ability in solving algebraic equations of higher degree clearly emerges from his works entitled Liber Quadratorum and Flos, both of which appeared in 1225. The first contains formulas and equations involving perfect squares, the second owes its fame to the irrational solution of a cubic equation, which Fibonacci determined with an accuracy of 10^-9. Most of his solving techniques seem to be based on the algebraic works of al-Khwarizmi.

Fibonacci initiated the tradition of the maestri d'abaco, experts in practical algebra and arithmetic, who flourished in Italy during the 14th century, and can be considered as the forerunners of Cardano, Tartaglia, and Ferrari.

Fibonacci Number, Fibonacci Sequence

Additional biographies: MacTutor (St. Andrews)