The rabbit breeding problem that caused Fibonacci to write about the sequence in Liber abaci may be unrealistic but the Fibonacci numbers really do appear in nature. For example, some plants branch in such a way that they always have a Fibonacci number of growing points. Finally, next time you look at a sunflower, take the trouble to look at the arrangement of the seeds. They appear to be spiralling outwards both to the left and the right. It seems that this arrangement keeps the seeds uniformly packed no matter how large the seed head.
Nature uses spirals to prevent overcrowding.
The Fibonacci numbers are studied as part of number theory and have applications in the counting of mathematical objects such as sets, permutations and sequences and to computer science. Acknowledgements This article was based on material written by Dr R. Knott , a lecturer in the Department of Computing Studies at the University of Surrey and additional material by Dr D. A. Quinney , a lecturer in the Department of Mathematics, University of Keele. Which is simply the rule for generating the Fibonacci numbers.