Fibonacci

Fibonacci  numbers report

 0,1,1,2,3,5,8,13,21,34,55,89,144,...

The Fibonacci number system springs from a man named Leonardo de Pisa. Most people call him Fibonacci.  Many years ago, he wrote a mathematics book, and in it, he wrote this question:

"A certain man put a pair of rabbits in a place surrounded by a

wall. How many pairs of rabbits can be produced from that pair

in a year if it is supposed that every month each pair begets a new pair from which

the second month on becomes productive?"

After some thinking on the question, Fibonacci came up with this sequence:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…

This is what we call the Fibonacci sequence.

The Fibonacci numbers look something like what you see above.  The sequence repeats itself over and over again. If you look closely at the sequence above, you can see the pattern: add the number behind. An interesting fact about this very old sequence of numbers is that it also appears in nature. For example: Branches, ferns, pinecones, flowers, leaves, even snail shells!

Fibonacci numbers also appear in the description of the reproduction of a population of idealized honeybees, according to the following rules:

§  If an egg is laid by an unmated female, it hatches a male or drone bee.

§  If, however, an egg was fertilized by a male, it hatches a female.

Thus, a male bee will always have one parent, and a female bee will have two.

If one traces the ancestry of any male bee (1 bee), he has 1 parent (1 bee), 2 grandparents, 3 great-grandparents, 5 great-great-grandparents, and so forth. This sequence of numbers of ancestors is the famous and mind boggling Fibonacci sequence. The number of ancestors at each level is the number of female ancestors, which is F_n−1, plus the number of male ancestors, which is F_n−2. (This is under the unrealistic assumption that the ancestors at each level are otherwise unrelated.)