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 puzzle that Fibonacci posed was how many pairs will there be in one year? When attempting to solve this problem, a pattern is detected:
Figure 1: Recognizing the pattern of the "rabbit problem".
If we were to keep going month by month, the sequence formed would be 1,1,2,3,5,8,13,21 and so on. From here we notice that each new term is the sum of the previous two terms. The set of numbers is defined as the Fibonacci sequence. Mathematically speaking, this sequence is represented as:
The Fibonacci sequence has a plethora of applications in art and in nature. One frequent finding in nature involves the use of an......
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