# Leonardo of Pisa

**Leonardo of Pisa** or **Leonardo Pisano** (c. 1170 - 1250), also known as **Fibonacci**, was an Italian mathematician and 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).

## Biography

Leonardo's father Guilielmo (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 learnt about the Arabic numeral system which the Muslims had learned from Hindu India and further developed.

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*. This book 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.)

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.

## Important publications

*Liber Abaci*(1202), a book on calculations.*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 problems, that is, problems involving Diophantine equations.*Di minor guisa*(on commercial arithmetic; lost)*Commentary on Book X of Euclid's Elements*(lost)

## Important contributions

## External links

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