Fibonacciszám

Fibonacciszám refers to the numbers in the Fibonacci sequence, a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. The sequence begins: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. The mathematical definition is recursive: F(0) = 0, F(1) = 1, and F(n) = F(n-1) + F(n-2) for n > 1.

The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics, although it had been described in Indian mathematics centuries earlier. The sequence appears in various natural phenomena, such as the branching patterns of trees, the arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of an artichoke, an uncurling fern, and the arrangement of a pine cone's bracts.

The ratio of successive Fibonacci numbers approximates the golden ratio (phi, approximately 1.618). This close relationship with the golden ratio has led to its appearance in art, architecture, and design. Fibonacci numbers have applications in computer algorithms, such as the Fibonacci search technique and Fibonacci heaps. They are also used in financial market analysis, though their predictive power is debated. The concept is a fundamental example of recursion and has significant implications in number theory and discrete mathematics.