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Tuesday, December 24, 2013

Rabbits Galore!

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This is the image I posted in the last entry. Now I want to go through it with you so you can see how exactly this pattern leads to the Fibonacci sequence.

Recall that the premise of Fibonacci's question was this:

1. You begin with one male rabbit and one female rabbit. These rabbits have just been born.
2. A rabbit will reach sexual maturity after one month.
3. The gestation period of a rabbit is one month.
4. Once it has reached sexual maturity, a female rabbit will give birth every month.
5. A female rabbit will always give birth to one male rabbit and one female rabbit.
6. Rabbits never die.

Ok, some of these may be a bit of a stretch, but let's just go with it. What do we have in Month #0 (the very start)?

Month 0: There is ONE pair of rabbits.

Month 1: The two rabbits have mated, but are not yet ready to give birth. Therefore, there is still just the ONE pair.

Month 2: Babies! But note Rule #5 - the female always gives birth to a pair of rabbits, so now we have TWO pairs.

Month 3: The original pair gives birth again (see #4), but the newest pair is now only able to mate. They will need to wait one more month before giving birth. So now we have THREE pairs.

Month 4: Finally, BOTH pairs of rabbits give birth and we now have FIVE pairs.

Month 5: Here is where it gets a little tricky, but by now, we have three pairs that are able to give birth and do so, leaving us with a total of EIGHT pairs of rabbits.

1, 1, 2, 3, 5, 8.... So develops the Fibonacci sequence. In my next post, we'll look at honeybees, and how they build their colonies. The process is quite different, but a) the result is the same, and b) unlike these hypothetical rabbits, the bees are real.

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