Fibonacci (c.1175–1250)

Fibonacci was the pen name of Leonardo of Pisa, one of the greatest mathematicians of the Middle Ages. The son of a Pisan merchant who also served as a customs officer in North Africa, he traveled widely in Barbary (Algeria) and was later sent on business trips to Egypt, Syria, Greece, Sicily, and Provence. In 1200 he returned to Pisa and used the knowledge gained on his travels to write Liber abaci (The Book of the Abacus), published in 1202, which introduced to western Europe the Hindu-Arabic numerals and decimal number system that remain in use today. The first chapter of Part 1 begins:


These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with this sign 0 which in Arabic is called zephirum, any number can be written, as will be demonstrated.


Fibonacci also showed he was capable of some amazing feats of calculation. For example, he found the positive solution of the cubic equation x3 + 2x2 + 10x = 20 using the Babylonian number system with base 60 (a strange choice, in view of his public advocacy of the decimal system!). He gave the result as 1; 22, 7, 42, 33, 4, 40 which is equivalent to


1 + (22/60) + (7/602) + (42/603) + (33/604 + (4/605 + (40/606)


How on Earth he obtained this, nobody knows; it was 300 years before anyone else could obtain such accurate results. As well as serious mathematics, Liber Abaci contains many playful passages and it is for one of these, concerning a problem about counting the offspring of a pair of rabbits, that Fibonacci became best known after Edouard Lucas called the sequence of numbers discussed by the rabbit problem the Fibonacci sequence.