The Golden Proportion

The Divine Proportion

The Golden section or the Divine Proportion is a visual representation of a number called Phi (pronouned fi). Phi is a number produced by bisecting a line at a particular time. Phi is 1.618033988749895, or by the numerical sequence called the Fibonacci Sequence.

The Phi is Evident everywhere in the universe - Nature, Space, Physics, Mathematics, Art and Design. Phi creates the Divine Proportion ( so called by the renaissance artist because of its abundance in the known universe, they thought it was created by God.)

Fibonacci Series

Leonardo Fibonacci discovered the series which converges on phi. In the 12th century he discovered a simple numerical series that is the foundation for an incredible mathematical relationship behind phi.

Starting with 0 and 1; each new number in the series is simply the sum of the two before it.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,.....

The ratio of each successive pair of numbers in the series approximates phi (1.618...) as 5 divided by 3 is 1.666...., and 8 divided by 5 is 1.60

A Brief History of the Golden Ratio

No one knows for certain exactly when the Golden Ratio was first discovered. Many believe that throughout history different ancient peoples discovered it; may have called it by different names.

Example of the Golden Ratio and its applications throughout history include:

1. The Egyptians in the design of the pyramids as early as 2575 B.C

2. The Greeks in the design and proportions used in building the Parthenon from 448 - 432 B.C.

3. Ancient Greek artists such as Phidias (500 - 432 B.C ) and philosophers including Plato (428 -347 B.C) studied and used the Golden Ratio in their works.

4. In his thirteen volume work Elements the mathematician Euclid, referred to a dividing line at the point of 0.6180399. He explained it as the way to divide a line in the extreme and mean ratio. Euclid wrote Elements in approximately 300 B.C

5. The Fibonacci Series was discovered in 1200 A.D

Prove it !

Don't believe it? Take honeybees, for example. If you divide the female bees by the male bees in any given hive, you wlii get 1.618. Sunflowers , which have opposing spirals of seeds have a 1.618 ratio between the diameters of each rotation. This same ratio can be seen in relationships between different components throughout nature.

Still don't believe it? Need something's that easily measured? Try measuring from your shoulder to your fingertips,and then divide this number by the length from your elbow to your fingertips. Or try measuring from your head to your feet, and divide by that the length from your belly button to your feet. Are the results the same? Somewhere in the area of 1.618?

The golden ratio is seemingly unavoidable.