Elements of Design
The Golden Mean - Proportion /5
In the pentagon, there is a Golden Section relationship between any diagonal and any side of the pentagon. AC :AB = ¢. All the diagonals intersect each other according to the Golden Section, so that AD :DE = and CE :ED = f. The smaller, inner pentagon formed by the diagonals contains similar relationships which can be expressed by +.
It is easy to understand why the Greeks thought the pentagon such a perfect shape and used it as a sacred symbol.
In the 
rectangle the ratio between the two sides is 1.618:1. This rectangle has
a number of peculiarities. If you construct a square on its longer side,
as shown on page 2, the square taken together with the rectangle will
form a new, larger rectangle.
In diagram the ratio between the long side M and the
short side m is the same ratio between the long and the short sides of
the larger rectangle.
We can show that the two ratios are the same by writing M:m = (M +m):M.
This is a mathematical proportion. There are also arithmetical
relationships in F.
If you divide by you will get 0.618. If you multiply by itself the result
will be 2.618. Compare these two figures with and you will notice something
strange about their relationship.
Notes Taken from "Looking and Seeing 3 - THE SHAPES WE NEED"
by Kurt Rowland ©1965 (out of publication)