Gold9472

03-05-2005, 03:35 PM

What is Phi?

Gold9472: I read about this in the DaVinci Code, and I thought it was incredible.

http://home.comcast.net/~gold9472/vitruvianman.gif

Leonardo DaVinci's "The Vitruvian Man"

Phi ( = 1.618033988749895... ), most often pronounced fi like "fee" 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 () 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:

http://goldennumber.net/images/goldprop.gif

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 can be derived through:

A numerical series discovered by Leonardo Fibonacci

Mathematics

Geometry

Phi appears in:

The proportions of the human body

The proportions of many other animals

Plants

DNA

The solar system

Art and architecture

Music

Population growth

The stock market

The Bible and in theology

Gold9472: I read about this in the DaVinci Code, and I thought it was incredible.

http://home.comcast.net/~gold9472/vitruvianman.gif

Leonardo DaVinci's "The Vitruvian Man"

Phi ( = 1.618033988749895... ), most often pronounced fi like "fee" 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 () 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:

http://goldennumber.net/images/goldprop.gif

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 can be derived through:

A numerical series discovered by Leonardo Fibonacci

Mathematics

Geometry

Phi appears in:

The proportions of the human body

The proportions of many other animals

Plants

DNA

The solar system

Art and architecture

Music

Population growth

The stock market

The Bible and in theology