The Golden Mean


The Golden Mean (or Golden Section), represented by the Greek letter phi, is one of those mysterious natural numbers, like e or phi, that seem to arise out of the basic structure of our cosmos.

Unlike those abstract numbers, however, phi appears clearly and regularly in the realm of things that grow and unfold in steps, and that includes living things.

The decimal representation of phi is 1.6180339887499…

The golden mean, Phi, has been applied in diverse situations in art, architecture and music, and although some have claimed that it represents a basic aesthetic proportion.

Others have argued that it is only one of a large number of such ratios. We review its early history, especially its relationship to the Mount Meru of Pingala.

We examine the successive divisions of 3, 7, and 22 in Indian music and suggest derivation from variants of Mount Meru. We also speculate on the neurophysiological basis behind the sense that the golden mean is a pleasant proportion.

In pure mathematics, an increase in size can be any imaginable number, even one like e or phi. But in the world of nature.

Things always grow by adding some unit, even if the unit is as small as a molecule. So it’s not surprising that phi turns out to be an ideal rate of growth for things which grow by adding some quantity.

Some examples:

The Nautilus shell (Nautilus pompilius) grows larger on each spiral by phi.

The sunflower has 55 (see number list) clockwise spirals overlaid on either 34 or 89 (see number list) counterclockwise spirals, a phi proportion.

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