The Fibonacci Sequence

Topics: Fibonacci number, Fibonacci, Golden ratio Pages: 2 (642 words) Published: September 23, 2013

The Fibonacci sequence
The Fibonacci sequence is a series of numbers developed by Leonardo Fibonacci as a means of solving a practical problem. The original problem that Fibonacci investigated, in the year 1202, was about how fast rabbits could breed in ideal circumstances. Suppose a newly born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair, one male, one female, every month from the second month on. The question that Fibonacci posed was how many pairs will there be in one year? At the end of the first month, they mate, but there is still one only 1 pair. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs. The Fibonacci sequence is the series of numbers, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89… When squares are made with the widths, you get a nice spiral. If you look closely at the center of a daisy, you will find that the yellow center is not solid. It is made up of sets of spirals that go out from the center. Mathematics is found in nature all the time. If you look at the bottom of a pinecone you will see that it has those same kinds of spirals. They don’t go around and around in a circle they go outward in the same sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89… While the symmetry of Fibonacci spiral patterns have often attracted scientists, a mathematical for their common occurrence in nature is not been discovered. Scientists have recently successfully produced Fibonacci spiral patterns in a lab,...

References: Wikipedia, the free encyclopedia -
Ball, Keith M (2003), "8: Fibonacci 's Rabbits Revisited", Strange Curves, Counting Rabbits, and Other Mathematical Explorations, Princeton, NJ: Princeton University Press
Lisa Zyga,  May 01, 2007 PHYS.ORG News
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