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Sunflowers, daisies, marigolds, dahlias, and many other plants flower in unique patterns, which obey a number of subtle mathematical relationships.

The seed and flower heads of these plants develop in two sets of spirals that emanate from the center—one curving clockwise and the other anti-clockwise. The head of the thistle below, for instance, has 21 rows spiraling out clockwise and 13 rows anti-clockwise. And sunflowers have numbers like 21 and 34 or 55 and 34.

These numbers are not random. They occur next to each other in a sequence known as Fibonacci Numbers. Each successive number, except for the first, is the sum of the previous two: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 etc. Fibonacci, an Italian mathematician, discovered the sequence in the thirteenth century.

This genetically determined pattern of growth can also been seen in pinecones, pineapples, artichokes, and many other plants.



Thistle
 


Purple coneflower

Birgit Reinert

 
Fleming, A.J. Plant mathematics and Fibonacci's flowers. Nature 418, 723 (August 15, 2002).
 
Klar, A.S. Plant mathematics: Fibonacci's flowers. Nature 417, 595 (June 6, 2002).
 

 

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