Phi for Neo-phi-tes
 What is Phi?
Phi ( Φ
= 1.618033988749895...
), pronounced fi like "fly," is simply an irrational number like pi (
p = 3.14159265358979... ), but one with many unusual
mathematical properties.
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 "Golden Section" and to Renaissance
artists as the "Divine Proportion"
It is also called the 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 (Φ)
is simply the ratio of the line segments
that result when a line is divided in one very special
and unique way.
Divide a line
so that:
the ratio of the length of the entire
line (A)
to the length of larger
line segment (B)
is the same as
the ratio of the length of the larger
line segment (B)
to the length of the smaller
line segment (C).
This happens only at the point where:
A is 1.618...
times B and B is
1.618... times C.
Alternatively, C is
0.618... of B and B is
0.618... of A.
Phi
with an upper case "P" is 1.6180339887..., while phi with a lower
case "p" is 0.6180339887, the reciprocal of Phi and also Phi
minus 1.
What makes
phi even more unusual is that it can be derived in
many ways and shows up in relationships throughout the universe.
Phi Φ can be derived through:
 Phi Φ appears in:
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