VI.6 Leonardo of Pisa (known as Fibonacci)

b. Pisa, Italy, ca. 1170; d. Pisa, Italy, ca. 1250

Son of Pisan merchant; studied mathematics under Muslim teachers in North Africa and traveled throughout the Mediterranean meeting with Islamic scholars; awarded an annual stipend in 1240 by the city of Pisa in recognition of his teaching and other services

One of the earliest European writers on algebra, Fibonacci is most famous for his Liber Abaci (“Book of calculation”), which first appeared in 1202 and was largely responsible for the spread of the Hindu–Arabic numerals throughout Europe. The book contained not only rules for computing with the Hindu–Arabic numerals but also a large number of problems of various kinds, the best known of which was his “rabbit problem.” This problem asks how many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair produces a new pair which becomes productive from the second month on. The number F_n of pairs there will be in the nth month is the number of pairs there were in the previous month plus the number of breeding pairs, and the latter is the number of rabbits there were in the previous month but one. This leads to the rule F_n = F_{n − 1} + F_{n − 2}. Starting with F₀ = 0 and F_l = 1, we obtain the sequence 0, 1, 1, 2, 3, 5, 8, 13,. . . of Fibonacci numbers. It can be shown that lim_{n → ∞} F_n+l/F_n = , where = (1+ ) / 2 is the golden ratio.