Tuesday, April 03, 2007

The popularity of the golden spiral

by David Yuri

Not many people know this, but there are lots of signs which are considered to be the cornerstone of life throughout the cosmos. The first and most important shape is the perfect circle. Seven circles passing through their centers create the shape known as the seed of life. If the seed of life would be multiplied, the shape thus obtained represents the flower of life. The centers of the seed of life, if connected, would form the shape known as the tree of life. All these shapes and many more are believed to contain the map of the universe and to represent the origin of life. All of them can be found in nature in one way or another.

Another symbol of this nature is the golden spiral. Two well known sacred geometry shapes are represented in the golden spiral: the Fibonacci spiral and the golden mean spiral. The golden mean, in philosophy, especially Aristotle's, represents the desirable middle between two extremes, one of deficiency and one of excess. The golden mean, phi, is also called the golden ratio or the golden proportion. It is a constant value that is more mysterious and profound than pi.

To obtain the golden ratio, one must divide a segment, for example AB, in a place, C, so that the ratio of the entire segment to the larger part of it is the same as the ratio of the larger segment to the smaller one. The decimals of the value phi keep on going, without repeating themselves. This unique number can be found incorporated in all organic structures, ranging from the bone structure of humans to the spiral of the shell sea. The presence of this ratio in all biological structures makes it seem like the blueprint for life. It was named by Plato the "key to the physics of the cosmos".

The value of phi is 1.6180339.... A structure that is based on the golden ratio is the golden rectangle and it was developed by the Greek mathematician Pythagoras. It is basically a rectangle that can be divided in a square and another rectangle that maintains the same proportions as the original rectangle. This type of rectangle can only be obtained based on the golden ratio. If you would add other squares on the longer sides of the golden rectangle, the shape obtained is another golden rectangle.

The Fibonacci sequence was used to describe the growth patterns of plants. It starts with 1, 1 and the next terms are obtained by adding the last two numbers, like this 2, 3, 5, 8, 13 and so on. The relationship of the Fibonacci sequence with the golden ratio is that if you were to divide the last number to the one before it, the value approaches the golden ratio. If you go further down the sequence, the value gets closer and closer, but it doesn't reach the exact value of phi.

The Fibonacci sequence can be represented in a spiral form. This is very similar, almost identical, to the golden spiral. The difference between the spiral obtained using the Fibonacci sequence and the golden spiral is the definite beginning of the first one. The golden spiral has no beginning and no end. A representation of the golden spiral was found in a crop circle in England, called the "Hackpen Hill formation".

A Fibonacci spiral shape can be found in Egypt. The positions of the centers of the Giza pyramids accurately define a line as the Fibonacci spiral. Also the phi ratio is found in the architecture of the Great Pyramid. The golden section is demonstrated in the basic cross section. Bottom line, the shape has great value and significance to it. The shape of spiral can be offered as a gift with great significance. If you consider offering someone jewelry representing this shape be sure to visit ka-gold-jewelry.com.


http://www.goarticles.com/cgi-bin/showa.cgi?C=447586

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