fibonacci-numbers

In order to study Fibonacci numbers, Fibonacci investigated a problem about growth
rate of rabbit population in a biologically unrealistic situation. The puzzle Fibonacci posed was:
assume that a newly born pair of rabbit, a male and a female is to be mate at the age of one
month to produce another pair of rabbit with a male and a female on the second month.
Assume that rabbits never die and the same cycle repeats every month so that all pairs give
birth to a new pair every month and a newly born pair can start mating from the second month.
How many pairs of rabbit will there be at the end of the year The solution of the problem
looks like the following:
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 making 2 pairs of rabbits.
At the end of the third month, the original female produces a second pair, making 3 pairs.
At the end of the fourth month, the original female has produced another new pair, the
female born two months ago produces her first pair as well, making 5 pairs.
If this cycle continues, at the end of n month, number of pairs will be the sum of number of
pairs in the month 2 and 1. This is same as the Fibonacci number (Knott, Fibonacci
Numbers and Nature, 2008).
The Fibonacci numbers are represented by the numbers in the following sequence. By
definition, the first two numbers in the Fibonacci series are 0 and 1, and the rest are the sum of
the previous two numbers.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …
Fibonacci numbers Page 3