Home #1 Mathematics Can we enumerate pineapple whorls?
Can we enumerate pineapple whorls? PDF Print E-mail
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Wednesday, 20 January 2010 00:00

Yes and there are still involved the "magic" Fibonacci numbers are involved.

Of course the answer involves several figures in nature, like Flowers or leaves.

We show an example about the "Margaret flower"

and the rose,

The mathematics involved may be stated as follows.

Please consider, Pn, the stages which moving point reaches at the equidistant moments which are equidistributeded like the helix stairs on a winding staircase. Now, if the angle of rotation of the operation s is a fraction u/v of the full angle 360" will be of the form,

1/1, 1/2, 2/3, 3/5, 5/8, 8/13, 13/21, 21/34 ...

in other words will be the Fibonacci numbers.

This discipline of Geometry is called Phyllotaxis, and was introduced and studies by German Wiser, Goethe as well Charles Bonnet, from 1754.

Explanations are more interesting that this, but I prefer interested people to consult the books:

Thanks,

Giovanni A. Orlando.

 

Last Updated on Wednesday, 20 January 2010 10:22