Leonardo of Pisa: Bunny Rabbits to Bull Markets

Editor’s note: This article was published in September 2005.

The year 2002 marked the 800th anniversary of the publication of a breakthrough mathematics book, Liber abaci (Book of Calculation) by Leonardo of Pisa, in Italy. It supported a dramatic simplification of arithmetic; the way numbers were recorded and manipulated. The book begins:

The nine Indian figures are: 9 8 7 6 5 4 3 2 1. With these nine figures,
and the sign 0 ... any number may be written, as demonstrated below.

In 1202, Europe was quite different than it is today. Given the state of transportation at the time, international trade thrived over water even more than land. Air travel remained the domain of birds, bats and bugs. European merchant sailors enjoyed a flourishing trade in exotic goods along Mediterranean ports. These goods included spices from the East as well as goatskins from North Africa for tanning into leather in Italy. One result was that maritime trade created prosperous Italian city-states. Merchants' business transactions and records were cumbersome, though. Accountants calculated with an abacus and recorded their results in Roman numerals. They needed a better way and Leonardo was destined to help provide it.

Leonardo, dubbed "a solitary flame of mathematical genius during the Middle Ages," was the precocious son of a merchant sailor and diplomat, Guilielmo Bonacci. Leonardo is now more commonly called Fibonacci, meaning son of Bonacci (Latin filius Bonacci), although this name was not applied to him until the nineteenth century. Fibonacci was born in Pisa, Italy, just a few years before construction began on the famous Leaning Tower of Pisa. (In fact, his statue may be found on the plaza of the tower today.)

In his early years, Leonardo accompanied his father to Bugia (now Bejaia in Algeria) where he served as the director of the Pisan trading colony. Leonardo's father provided an Arab tutor to instruct him in Indian numerals and computation. Leonardo later traveled widely among Mediterranean ports in Egypt, Greece and Syria. Along the way he studied the works of more mathematically sophisticated Eastern cultures.

Liber abaci mainly illustrated routine calculations to solve practical problems in the new number system. Merchants needed a better way to keep accounts and exchange foreign currencies. The solutions offered in the book reveal Hindu influences of Brahmagupta and Bhaskara in methods of ratio and proportion along with Islamic influences of al-Khwarizmi and Abu Kamil with rhetorical (not yet symbolic) algebra.

After returning to Italy, Fibonacci was awarded a stipend for advising the Republic of Pisa in accounting and related mathematical matters. By decree, the Republic awarded the "'serious and learned Master Leonardo a yearly salarium of 'libre XX denariorem' in addition to the usual allowances."

Lesson Plan 1