A method to construct a golden rectangle. The square is
outlined in red. The resulting dimensions are in the golden ratio.
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... .
THIS IS ALSO CALLED "THE DIVINE PROPORTION"
that of Aristotle
, the golden
mean is the desirable middle between two extremes, one of excess and the
other of deficiency. For example courage, a virtue, if taken to excess would manifest as
recklessness and if deficient as cowardice.
To the Greek mentality, it was an attribute of beauty. Both ancients and
moderns realized that there is a close association in mathematics between beauty
. The poet John Keats
, in his Ode on a Grecian
, put it this way:
"Beauty is truth, truth beauty," -- that is all..Ye know on earth, and all
ye need to know.
In Chinese philosophy, a similar concept, Doctrine of the Mean, was propounded by Confucius; Buddhist philosophy also
includes the concept of the middle
The Divine Proportion was closely studied by the Greek sculptor, Phidias, and
as a result, it took on the name of Phi. Also referred to as the Golden Mean,
the Magic Ratio, the Fibonacci Series, etc., Phi can be found throughout the
universe; from the spirals of galaxies to the spiral of a Nautilus seashell;
from the harmony of music to the beauty in art. A botanist will find it in the
growth patterns of flowers and plants, while the zoologist sees it in the
breeding of rabbits. The entomologist views it in the genealogy of a bee, and
the physicist observes it in the behavior of light and atoms. A Wall Street
analyst can find it in the rising and falling patterns of a market, while the
mathematician uncovers it in the examination of the pentagram.
The Greeks believed there to be three 'ingredients' to beauty: symmetry,
proportion, and harmony. This triad of principles infused their life. They were
very much attuned to beauty as an object of love and something that was to be
imitated and reproduced in their lives, architecture, education (Paideia
) and politics. They judged life
by this mentality.