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in reply to Rabbits
Umm, nice ASCII art, and all, but the whole rabbits thing isn't the fibonacci sequence, is it?
If I start with two rabbits, and each pair produces two more each month, then I'll end up with 2, 4, 8, 16, 32, 64... rabbits after each month.
Won't I? |
Re^2: Rabbits
by CloneArmyCommander (Friar) on Nov 29, 2004 at 13:55 UTC
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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 ;). | [reply] |
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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 ? ;)
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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.
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Well, that's that clarified. The monthly thing was misleading me :)
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