Mother Nature knows her math. The seeds of plants with spiral patterns form interlocking spirals in both clockwise and counterclockwise directions. The number of clockwise spirals differs from the number of counterclockwise spirals.
These numbers have a remarkable consistency. They are almost always two consecutive Fibonacci numbers, which are another one of nature's mathematical favorites. The Fibonacci numbers form the sequence 1, 1, 2, 3, 5, 8, 13, 21 . . . , in which each number is the sum of the previous two.

Flowers, cones, and cacti have other mathematical wonders that scientists are trying to understand and explain. Link -via Metafilter

http://goldennumber.net is a good site to research Fibonacci Serie and Golden Ratio (phi)
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Along these lines...

I was in Paris in October with my folks. We saw this strange and beautiful vegetable at a farmer's market on the street:

Strange Vegetable Pic

What sort of mathematics are behind something like that?

P.S. I think it was some sort of cauliflower.
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If you have access to the scientific journal Applied Physics Letters (through a university or other subscription), there is a neat article by some scientists who have recently managed to recreate the Fibonacci spiral pattern by self-assembly in the laboratory. They suggest it comes about as a result of energy minimization on the surface of a cone, which is why it would appear so often in nature (less energy spent growing = more energy devoted to survival).

Clicky
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"The Mathematical Lives of Plants."

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