The Golden Ratio

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The golden ratio is another fundamental measure.   (The golden ratio is about 1.618033988749894848204586834365638117720309180…) The golden ratio is the unique ratio such that the ratio of the whole to the larger portion is the same as the ratio of the larger portion to the smaller portion.

the golden ratio 1the golden ratio

The golden ratio (phi) has some unique properties and makes some interesting appearances:

  • phi = the ratio of segments in a 5-pointed star (pentagram) considered sacred to Plato and Pythagoras in their mystery schools. Note that each larger (or smaller) section is related by the phi ratiogolden ratio 2

Spirals

This spiral generated by a succession of Golden Triangles (triangles with relative side lengths of 1, phi and phi) is the classic shape of the Chambered Nautilus shell. The creature building this shell uses the same proportions for each expanded chamber that is added; growth follows a law which is everywhere the same. The outer triangle is the same as one of the five “arms” of the pentagonal graphic above.

spiral 1spirals

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