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
What is Phi?
Phi ( = 1.618033988749895... ), most often pronounced fi like "fly", is simply an irrational number like pi ( p = 3.14159265358979... ), but one with many unusual mathematical properties. Unlike pi, which is a transcendental number, phi is the solution to a quadratic equation.
Phi is the basis for the Golden Section, Ratio or Mean
The ratio, or proportion, determined by Phi (1.618 ...) was known to the Greeks as the "dividing a line in the extreme and mean ratio" and to Renaissance artists as the "Divine Proportion". It is also called the Golden Section, Golden Ratio and the Golden Mean.
Phi, like Pi, is a ratio defined by a geometric construction
Just as pi (p) is the ratio of the circumference of a circle to its diameter, phi () is simply the ratio of the line segments that result when a line is divided in one very special and unique way.