THE GOLDEN MEAN (Φ)

by Nikhat Parveen, UGA

 

 

 

The Golden Mean (or Golden Section), represented by the Greek letter phi, is one of those mysterious natural numbers, like e or pi, 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...
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How to Construct a Golden Section?

A golden section may be constructed in several ways. The following method of construction is one of them:

Draw a line segment AB of length a on the straight line PQ.

Now construct a perpendicular BD of length a at B. Bisect AB at E with E as the centre and ED as the radius, describing an arc that intersects PQ at C.

Then by Pythagoras theorem, the radius

We have,

Here, AC is divided in the golden ratio by the point B.

 

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