Re^2: Rabbits

[CloneArmyCommander]

That's the story behind that Fibonacci sequence. I forget the exact details, but many years ago Fibonacci was given this problem, "If I have two rabbits. . . " and the solution he found was, 1,1,2,3,5,8,.... It also gave me an image to use :). Another interesting thing is that things in nature, such as flowers, seem to show numbers relating to the sequence. Almost all flowers have a number of petals that is a number in the Fibonacci sequence :) (normally, pluck a few out, and I might be wrong ;).

[zejames]

Let's assume that each couple of rabbits give birth to two baby rabbits.

Let's count the number of couple of rabbits. At the beginning, we've 1 couple of young rabbit

F_1 = 1

Next year, they'll be adult rabbits, but won't have children yet :

F_2 = 1

On the third year, they'll a two baby rabbits, that is one couple

F_3 = 2

On the forth year, the first parent will have two baby rabbits again, but young rabbits won't be old enough to do so

F_3 = 2 + 1 = 3

On the fifth year, we've got two couples that can have little rabbits and one that cannot :

F_3 = 3 + 2 = 5

and so on... Each year, the number of couple is :

• the number of rabbits that lived the year before, that is F_{n-1}
• plus the number of rabbits that were born that year, that is the number of couple old enough to proceate, that is F_{n-2}

To conclude :

F_n = F_{n-1} - F{n-2}

Funny, isn't it ? Ok, that is not very realistic and very accurante, but who cares ? ;)

[CloneArmyCommander]

That's one way of putting it :). I find it fun to play around with sequences and series, and perl is just an easy language to model them with. Thanks for the clear picture and explanation :), I understood the idea, but it is difficult for me to explain.

[Jasper]

Well, that's that clarified. The monthly thing was misleading me :)