Definitions for fibonacci number
This page provides all possible meanings and translations of the word fibonacci number
a number in the Fibonacci sequence
Any number in a Fibonacci sequence (being the sum of the preceding two numbers)
In mathematics, the Fibonacci numbers or Fibonacci series or Fibonacci sequence are the numbers in the following integer sequence: By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two. In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation with seed values The Fibonacci sequence is named after Leonardo Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics. By modern convention, the sequence begins either with F0 = 0 or with F1 = 1. The Liber Abaci began the sequence with F1 = 1, without an initial 0. Fibonacci numbers are closely related to Lucas numbers in that they are a complementary pair of Lucas sequences. They are intimately connected with the golden ratio; for example, the closest rational approximations to the ratio are 2/1, 3/2, 5/3, 8/5, ... . Applications include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings, such as branching in trees, phyllotaxis, the fruit sprouts of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone.
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