Most of you know of the Fibonacci sequence. Its the magical sequence of numbers that was mentioned in the Da Vinci Code novel. I took it in school and university and never actually knew what it represented.
The original sequence was studied by an Indian mathematician called Virahanka in the 6th century AD. Virahanka was analyzing the length of sequences of long and short syllables in an ancient Indian language. The long syllable was twice as long as the short syllable. The Ith number in the Fibonacci sequence is the number of total combinations that can be composed of those two syllables with length equal to I.
For example:
If the short syllable is S (represents 1 unit of length) and long is L (represents 2 units of length) then for the 3rd number in the sequence the number of combinations of the two syllables that make a total unit length of 3 are:
{ SSS, SL, LS }
If you do this for lengths of 1,2,3,4,5,... you will find that the original Fibonacci sequence is created which is 1,2,3,5,8,13,21,...
Later on Leonardo of Pisa (AKA Fibonacci) studied the sequence of numbers and linked it to reproducing in rabbit populations to produce the sequence we know today which is summarized in the formula: F(n) = F(n−1) + F(n−2). Which is:
0,1,1,2,3,5,8,13,21...
Has anyone seen rabbits reproduce before? I had rabbits in my back yard when I was a kid. We bought two French rabbits (male and female) and two Egyptian rabbits (male and female). In about a year they had become an extended family of 18 and the number went up and up exponentially just like the Fibonacci sequence. Very often we would catch sight of a new born exploring its way outside of the burrow and race back in as we approached.
Yaaaaa...those were the days...
I came across the Fibonacci sequence the other day when I came across a question; It said, "Given that you can take one step or two steps forward from a given step, find the total number of ways of reaching the Nth step?"
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