Fibonacci Sequence - Golden Section Explained

The Fibonacci spiral is named after Italian mathematician Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been described earlier as Virahanka numbers in Indian mathematics. By modern convention, the sequence begins either with F0 = 0 or with F1 = 1. The sequence described in Liber Abaci began with F1 = 1.

Fibonacci numbers are closely related to Lucas numbers. They are intimately connected with the golden ratio or golden mean; for example, the closest rational approximations to the ratio are 2/1, 3/2, 5/3, 8/5, ...

Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly. Applications of Fibonacci numbers 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 arrangement of leaves on a stem), the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bracts. This movie also deals with the magical applications of the sequence, the pentagram or pentacle being a Fibonacci spiral borrowed directly from nature, and also many practical applications and mathematical ideas.