The golden ratio is a number used in mathematics, art, architecture, nature, and architecture. Also known as, the divine proportion, golden mean, or golden section it expresses the relationship that the sum of two quantities is to the larger quantity as is the larger is to the smaller. It is also a number often encountered when taking the ratios of differences in different geometric figures.
Represented mathematically as approximately 1.618033989, and by the Greek letter Phi, the number tends to show up frequently in geometrical shapes. For example, the golden ratio is the basis for the construction of a pentagram. This shape looks like a regular star; five straight lines form a star with five points. The pentagon within the star in the center is proportional to the points of the star by a ratio of 1: 1.618.
The golden ratio appeared so much in Geometry, as stated above with the pentagram example, that it intrigued the Ancient Greeks. They studied the ratio for most of the same reasons mathematicians study it today. They found it to have unique and interesting properties. It is said that the Parthenon, among other Greek architecture have many proportions approximate to the golden ratio. Other classical buildings and structures have been said to have been modeled off of the golden ratio, so it can be argued that the artists and architects who designed such things were aware of the golden ratio and used it to create an aesthetically pleasing design. However, it can be argued that such designers used their basic sense of good proportion. On the other hand, such analyses can always be questioned on the ground that the designer chooses the points from which the measurements are made and that these choices affect the proportions observed.
Personally, I think that the golden ratio is very interesting, but it does not have enough solid backing to be looked upon as a perfect proportionality between different things other than that of...