## Quick Reference

(*c.*1170–1250) Italian mathematician

Fibonacci lived in Pisa and is often referred to as Leonardo of Pisa. Although he was probably the most outstanding mathematician of the Middle Ages virtually nothing is known of his life. The modern system of numerals, which originated in India and had first been introduced to the West by al-Khwarizmi, first became widely used in Europe owing to Fibonacci's popularization of it. His father served as a consul in North Africa and it is known that Fibonacci studied with an Arabian mathematician in his youth, from whom he probably learned the decimal system of notation.

Fibonacci's main work was his Liber abaci (1202; Book of the Abacus) in which he expounded the virtues of the new system of numerals and showed how they could be used to simplify highly complex calculations. Fibonacci also worked extensively on the theory of proportion and on techniques for determining the roots of equations, and included a treatment of these subjects in the Liber abaci. In addition it contains contributions to geometry and Fibonacci later published his Practica geometriae (1220; Practice of Geometry), a shorter work that was devoted entirely to the subject.

Fibonacci was fortunate in being able to gain the patronage of the Holy Roman Emperor, Frederick II, and a later work, the Liber quadratorum (1225; Book of Square Numbers) was dedicated to his patron. This book, whch is generally considered Fibonacci's greatest achievement, deals with second order Diophantine equations. It contains the most advanced contributions to number theory since the work of Diophantus, which were not to be equaled until the work of Fermat. He discovered the *Fibonacci sequence* of integers in whch each number is equal to the sum of the preceding two (1, 1, 2, 3, 5, 8, …).

*Subjects:*
mathematics.