As easy as 1, 1, 2, 3 ... (Fibonacci Sequence)

"In 1964, an article in a journal called the Fibonacci Quarterly demonstrated that The Art of Fugue has a mathematical perfection - that in this composition, Bach exploits, in a final reach for the complex harmony that fascinated him all his life, a sequence of numbers that recurs again and again in the natural world and which has come to possess an almost mystical fascination not just for maths professors but for musicians, artists and architects.

The idea is simple enough. It originates in a problem that the medieval mathematician Leonardo of Pisa - nicknamed Fibonacci - posed in 1202 in his Liber Abaci (Book of the Abacus). Suppose that a single pair of rabbits in January breed a second pair by February. For every month after, both rabbits breed a pair of rabbits, and each new pair also produce a pair a month. How many pairs of rabbits are there in December?

A lot, would be my answer. Mathematicians, however, can see that Leonardo's rabbits produce a very special sequence of numbers in which each equals the sum of the two preceding in the series. If you begin with 0, then add 1, you get the next number, 0+1=1; the next after that is 1+1=2; then 1+2=3; and from there you get a rapid increase - the sequence runs 3, 5, 8, 13, 21, and so on, quickly reaching huge figures." (full article at link)

Useful links
The Fibonacci Sequence ensemble
The Fibonacci Association
The mathematical theory behind the Fibonacci numbers
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