Another great article from Wiki. I am immersing myself in puzzles and riddles now and will have some to post in the near future. Keep checking back.

The earliest known reference to Fibonacci numbers is contained in a book on meters by an Indian mathematician named Pingala called Chhandah-shastra (500 BC). As documented by Donald Knuth in The Art of Computer Programming, this sequence was described by the Indian mathematicians Gopala and Hemachandra in 1150, who were investigating the possible ways of exactly bin packing items of length 1 and 2. In the West, it was first studied by Leonardo of Pisa, who was also known as Fibonacci (c. 1200), to describe the growth of an idealised (although biologically unrealistic) rabbit population. The numbers describe the number of pairs in the rabbit population after n months if it is assumed that:

• in the first month there is just one newly-born pair,
• new-born pairs become fertile from their second month on
• each month every fertile pair begets a new pair, and
• the rabbits never die

Suppose that in month n we have a pairs of fertile and newly born rabbits and in month n + 1 we have b pairs. In month n + 2 we will necessarily have a + b pairs, because all a pairs of rabbits from month n will be fertile and produce a pairs of offspring, while the newly born rabbits in b will not be fertile and will not produce offspring.