fibonacci

Fibonacci refers to the Italian mathematician Leonardo of Pisa, known as Fibonacci, who lived circa 1170 to circa 1250. He played a key role in introducing Hindu-Arabic numerals to Europe through his book Liber Abaci (1202) and helped popularize decimal calculation in commerce. The surname Fibonacci means “son of Bonacci,” reflecting a family name used in his region.

The term also denotes the Fibonacci sequence, an integer sequence defined by F1 = 1, F2 = 1, and F(n) = F(n-1) + F(n-2) for n > 2. Some conventions use F0 = 0, yielding the initial terms 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. The sequence appears in various areas of mathematics and computer science, as well as in natural phenomena.

A notable property is that the ratio of successive Fibonacci numbers converges to the golden ratio φ ≈ 1.6180339. This connection underpins many approximate measurements in art and architecture, and Fibonacci numbers arise in biological settings such as the arrangement of leaves, seeds, petals, and the spirals seen in shells and pinecones.

In modern applications, Fibonacci numbers appear in algorithms and data structures, including the Fibonacci search technique and Fibonacci heaps. They also serve as a common topic in recreational mathematics and mathematical identities, illustrating the enduring influence of Fibonacci in both theory and practice.