In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation
F_n = F_{n-1} + F_{n-2}, with seed values[1][2] F_1 = 1, F_2 = 1 or F_0 = 0, F_1 = 1
Fibonacci pattern and nature:
Rabbits, Cows and Bees Family Trees
Let's look first at the Rabbit Puzzle that Fibonacci wrote about and then at two adaptations of it to make it more realistic. This introduces you to the Fibonacci Number series and the simple definition of the whole never-ending series.
Fibonacci's Rabbits
The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances.
Fluffy bunnies
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?
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.
(hint = this picture is 468x60 px)
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