PHI-Divine Proportion

This thread has been inspired by Dan Brown's-Da Vinci Code(A novel that left me flabbergasted!).

What is Phi?

Phi ( [​IMG] = 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 equaton.​
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#-Link-Snipped-#.​
[​IMG]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 ([​IMG]) 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 1.618 0339 887 ..., 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.​


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