8/7/2019 Fibonacci by Leonardo Da Pisa

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Fibonacci by Leonardo da Pisa

He was an Italian mathematician who was the first great Western mathematicianafter the decline of Greek science. The son of a merchant, Fibonacci drew the

motivation to mathematical inquiry1 from his commercial trips to the the Orient. Itwas 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 stillcurrent in Western Europe.

Performing even the simplest arithmetical operations with a non -positional notationwas a difficult endeavor 2: for this task the merchants were forced to resort to the

abacus, a device where the numbers were represented by moving balls. Fibonacciexposed 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 wasintended as an algebra manual for commercial use, and explained the arithmeticalrules using numerical examples derived, for example, from measur e and currency

conversion, which were translated into proportions and solved by multiplication(rule of three). The so-called Fibonacci sequence arose

3 in this book from a concre tequestion 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 Greekmathematics; it contains theorems from Euclid's Elements and also Heron's formulafor 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 hisroyal seat in Palermo. His striking 4  ability in solving algebraic equations of higher degree clearly emerges from his works entitled Liber Quadratorum and Flos, both ofwhich 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 techniquesseem 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  flourished5 in Italy during the 14th century, and can be

considered as the forerunners of Cardano, Tartaglia, and Ferrari.

1A question you ask in order to get information

2To try to do something new or difficult

3If a problem or difficult situation arises, it begins to happen

4Unusual and noticeable

5To develop or grow and be successful