All shapes, dimensions and many images used in designing this site conform
to the Golden Ratio or Golden Section.
Not to be confused with Golden Mean (philosophy), the felicitous middle
between two extremes, Golden Numbers, an indicator of years in astronomy
and calendar studies, or the Golden Rule.
The golden section is a line segment sectioned into two according to
the golden ratio. The total length a+b is to the longer segment a as
a is to the shorter segment b. In mathematics and the arts, two quantities
are in the golden ratio if the ratio between the sum of those quantities
and the larger one is the same as the ratio between the larger one and
the smaller. The golden ratio is approximately 1.6180339887 (from the
quadratic formula below).
At
least since the Renaissance, many artists and architects have proportioned
their works to approximate the golden ratio - especially in the form
of the golden rectangle, in which the ratio of the longer side to the
shorter is the golden ratio - believing this proportion to be aesthetically
pleasing. Mathematicians have studied the golden ratio because of its
unique and interesting properties.
The golden ratio can be expressed as
a mathematical constant, usually denoted by the Greek letter [phi].
The figure of a golden section illustrates the geometric relationship
that defines this constant. Expressed algebraically:
This equation has as its unique positive solution the algebraic irrational
number: