Wednesday, July 13, 2011

HOW I SEE MATHEMATICS

To see a World in a Grain of Sand, 
And a Heaven in a Wild Flower,
Hold Infinity in the Palm of your hand,
and Eternity in an hour.

-William Blake



The clockwise and counterclockwise spiraling florets of a sunflower's head grow in a way that affords the most efficient sharing of space.  Most commonly there are 34 spirals going one way and 35 going the other but ratios of numbers of spirals have been seen as 89/55, 144/89 and even 233/144 (size dependent of course).  All of these are ratios of adjacent Fibonacci numbers... the limit of these ratios will be the golden ratio, the most efficiently packed manner the flower could form.  
This is seen in most phyllotaxis, from branches on trees to rose petals, the beauty of geometrical and Fibonacci-based formations manifested in each flower.  This is mathematics.

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