Golden Sections

A golden section is a line segment that has been divided into two parts in such a way that the ratio of the longer part (a) to the shorter part (b) is equal to the ratio of the entire segment (a + b) to the longer part (a). This can be indicated symbolically as a/b = (a + b)/a = phi (Greek lower-case letter), and this ratio, phi, is called the golden ratio.

The concept of a golden section is of historical importance in aesthetics, art, and architecture. It has often been thought that a form, including the human form, is most pleasing when its parts divide it in golden sections. A related concept is the golden rectangle, which is a rectangle that has adjacent sides with lengths in the golden ratio.

The ancient Greeks felt that the golden rectangle had proportions that were the most aesthetically pleasing of all rectangles; the shape appears in many works from antiquity to the present. It is especially prevalent in Renaissance art and architecture. A golden rectangle has the property such that if a square with side equal to the rectangle’s short side is marked off, the remaining figure will be another golden rectangle; this process can be repeated indefinitely.