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...
.

**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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