The beauty of irrationality is easily demonstrated in this recursive construction of three geometric spirals. This particular construction uses the irrational number as defined by (1 + Math.sqrt(5) ) / 2, also called the Golden Mean. The approximation of this irrational is 1.618033...

Each spiral is generated using recursive attachments of the same geometric shape. In this example, polygons of sides 3, 4, and 5 have been used.

Click the NEXT button to view each spiral version. Right click, ZOOM IN to reveal the infinite nature of these constructions.

August 21, 2001

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