Portrait by unknown artist
|Born||c. 1170-75 in Pisa|
|Died||c. 1240 (aged around 70)
Most likely Pisa
|Known for||The Liber Abaci
The introduction of digital notation to Europe
Leonardo Pisano Bigollo (c. 1170 – c. 1250)—known as Fibonacci (Italian: [fiboˈnattʃi]), and also Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci—was an Italian mathematician, considered by some “the most talented Western mathematician of the Middle Ages.”
Fibonacci is best known to the modern world for the spreading of the Hindu–Arabic numeral system in Europe, primarily through his composition in 1202 of Liber Abaci (Book of Calculation), and for a number sequence named the Fibonacci numbers after him, which he did not discover but used as an example in the Liber Abaci.
Fibonacci was born around 1170 to Guglielmo Bonacci, a wealthy Italian merchant and, by some accounts, the consul for Pisa. Guglielmo directed a trading post in Bugia, a port in the Almohad dynasty‘s sultanate in North Africa. Fibonacci traveled with him as a young boy, and it was in Bugia (now Béjaïa, Algeria) that he learned about the Hindu–Arabic numeral system.
Alternatively, according to a history text by mathematician Tobias Dantzig, his father was “a lowly shipping clerk nicknamed Bonaccio, which, in the idiom of the period, meant ‘simpleton’ … hence ‘Fibonacci,’ the ‘son of a simpleton.'”
Recognizing that arithmetic with Hindu–Arabic numerals is simpler and more efficient than with Roman numerals, Fibonacci travelled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. He returned from his travels in around 1200, and in 1202, the 32-year-old recorded what he had learned in Liber Abaci (Book of Abacus or Book of Calculation), and thereby popularized Hindu–Arabic numerals in Europe.
Liber Abaci (1202)
In the Liber Abaci (1202), Fibonacci introduced the so-called modus Indorum (method of the Indians), today known as Arabic numerals (Sigler 2003; Grimm 1973). The book advocated numeration with the digits 0–9 and place value. The book showed the practical importance of the new numeral system by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interest, money-changing, and other applications. The book was well received throughout educated Europe and had a profound impact on European thought.
Liber Abaci also posed, and solved, a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century, but it was Fibonacci’s Liber Abaci that introduced it to the West.
In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers. Fibonacci began the sequence not with 0, 1, 1, 2, as modern mathematicians do but with 1,1, 2, etc. He carried the calculation up to the thirteenth place (fourteenth in modern counting), that is 233, though another manuscript carries it to the next place: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377. Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence.
There are many mathematical concepts named after Fibonacci, for instance because of a connection to the Fibonacci numbers. Examples include the Brahmagupta–Fibonacci identity, the Fibonacci search technique, and the Pisano period. Beyond mathematics, namesakes of Fibonacci include the asteroid 6765 Fibonacci and the art rock band The Fibonaccis.
- Liber Abaci (1202), a book on calculations (English translation by Laurence Sigler, Springer, 2002)
- Practica Geometriae (1220), a compendium of techniques in surveying, the measurement and partition of areas and volumes, and other topics in practical geometry (English translation by Barnabas Hughes, Springer, 2008).
- Flos (1225), solutions to problems posed by Johannes of Palermo
- Liber quadratorum (“The Book of Squares“) on Diophantine equations, dedicated to Emperor Frederick II. See in particular the Brahmagupta–Fibonacci identity.
- Di minor guisa (on commercial arithmetic; lost)
- Commentary on Book X of Euclid’s Elements (lost)