Fibonacci (c. 1170 - c. 1240), also known as Leonardo of Pisa, was an Italian mathematician of the Republic of Pisa and the most influential Western mathematician of the Middle Ages. [1] His book Liber Abaci of 1202 introduced the Hindu-Arabic numeral system and its methods of calculation to Latin-reading Europe. [2] A problem in that work gives the sequence now universally known as the Fibonacci numbers.
Life
Leonardo Bonacci, called Fibonacci, was born in Pisa around 1170, when the city was a leading Mediterranean trading republic. [1] His father, Guglielmo, was a Pisan merchant official posted to the North African port of Bugia (modern Béjaïa in Algeria), and the young Leonardo joined him there.
In North Africa he was taught calculation with the Hindu-Arabic numerals, and he continued to study mathematics on commercial travels around the Mediterranean, including Egypt, Syria, Greece, Sicily and Provence. [2] He compared the methods he encountered with the cumbersome Roman-numeral arithmetic then usual in Europe and concluded that the Indian system was far superior for practical computation.
Liber Abaci
Returning to Pisa, Fibonacci completed Liber Abaci ("Book of Calculation") in 1202, revising it in 1228. [1] The work sets out the nine Indian figures together with the symbol zero, explains place value, and demonstrates addition, subtraction, multiplication and division, fractions, proportions, currency conversion, profit and interest calculations, and methods for solving equations.
Much of the book is addressed to the practical needs of merchants, and its commercial examples helped the new numerals spread through Italian trading houses and then through Europe, gradually displacing Roman numerals and the counting board. [3]
The Fibonacci sequence
Among the exercises in Liber Abaci is a problem about the growth of an idealised population of rabbits. Its solution generates the series 1, 1, 2, 3, 5, 8, 13, 21 and so on, in which each term is the sum of the two preceding terms. [2] The sequence was known earlier to Indian scholars working on Sanskrit prosody, but Fibonacci's presentation carried it into European mathematics.
Nineteenth-century mathematicians named the series after him, and it has since been studied extensively, notably for the fact that the ratio of successive terms converges on the golden ratio. The numbers appear in combinatorics, number theory, computer algorithms and models of certain natural growth patterns. [3]
Other works and later life
Fibonacci wrote several further mathematical treatises, including Practica Geometriae on geometry and measurement, Flos, and Liber Quadratorum ("The Book of Squares"), a sophisticated work on number theory that is often considered his finest mathematical achievement. [1]
His reputation reached the court of the Holy Roman Emperor Frederick II, and he took part in mathematical problem-solving before the emperor's scholars. In 1240 the Republic of Pisa granted him a salary in recognition of his services to the city's accounting and instruction. He is thought to have died in Pisa around 1240 to 1250. [2]
Legacy
Fibonacci's work marks the point at which European mathematics adopted the computational tools of the Islamic and Indian traditions, a change that underpinned later commercial, scientific and mathematical development. [3] A statue of him stands in Pisa, and the sequence named after him remains one of the most widely recognised objects in mathematics.
