Fiboncciszámok

Fiboncciszámok, often referred to as Fibonacci numbers, form a sequence in which 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. Mathematically, the sequence can be defined by the recurrence relation F(n) = F(n-1) + F(n-2), with initial conditions F(0) = 0 and F(1) = 1.

This sequence was introduced to the Western world by Leonardo of Pisa, later known as Fibonacci, in his 1202 book Liber Abaci. He used it to model the growth of a rabbit population under idealized conditions. However, the sequence was described much earlier in Indian mathematics, in connection with Sanskrit prosody.

Fibonacci numbers appear in numerous areas of mathematics and nature. They are closely related to the golden ratio, approximately 1.618. The ratio of consecutive Fibonacci numbers approaches the golden ratio as the numbers get larger. This relationship explains their prevalence in patterns found in nature, such as the branching of trees, the arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of an artichoke, and the uncurling of a fern and the arrangement of a pine cone's bracts. They also have applications in computer algorithms, financial market analysis, and art.