In Mathematics, an infinite series of numbers beginning with 0,1 where each successive number is the sum of the two previous numbers.
A short beginning might be: 0,1,1,2,3,5,8,13.... ad infinitum.
The curious thing about this series of numbers is that it is found throughout nature. The Fibonocci series can be found in the spiral of seashells, the patterns of leaves on a tree, and the petals of flowers. It has been recognized and used in Art for centuries, where paintings were based upon it's composition (known as "The Golden Mean " or "Divine Proportion" - approximately 1.6180339887). The Parthenon in ancient Greece is based almost entirely on the proportions found within the golden mean, Da Vinci used it in "The Last Supper " and Michaelangelo used it in The Sistine Chapel . Note that there is nothing absolute about the Golden Mean - it merely defines a relationship within a set of numbers. The higher the numbers, the more precise the relationship. Televisions, letter pages, and business cards are but a few examples of it's use in popular culture.
Curious? Further Reading - http://goldennumber.net/