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       Originally this was a problem that he investigated (in the year 1202) to see how fast rabbits would breed in ideal circumstances. This was assuming that none of the rabbits died,  and that each pair of rabbits did not give birth to more than one pair of rabbits each month.

      The picture below shows a pair of rabbits that are born and don't mature until after the first month. After the first month they give birth to a pair of rabbits which don't mature until after the first month. It repeats this pattern continuously. If you look at the numbers at the right in the chart, it shows the number of rabbits that are alive at the time. These numbers are the Fibonacci Sequence. This is how he discovered the sequence.
 

        When you look at the sequence and pick a number you will notice it is composed of the previous two numbers added together. 1 + 1 = 2 ...  1 + 2 = 3...  2 + 3 = 5 and so on.  After this, more discoveries were made about how applicable this pattern is.  It was discovered that this pattern was found throughout nature and that it is a very pleasing pattern to humans in many different ways. 

      One important number that was found as a result of the Fibonacci sequence is 1.61803.  This number is called Phi, the Golden Ratio, and the Divine Number, it is the limit of the ratio of two consecutive Fibonacci numbers. Rationally represented it is (1+sqrt5)/2, which is one of the roots of the equation X^2=X-1. It is also used to construct the Golden Rectangle.  This is a pretty special number!  There will be a full discussion later about how this number is connected to nature and how we humans use it in our creations.