golden section

The golden section is the ratio a:b, equal to 8:13. A golden rectangle is one, like that shaded in the picture, that has its length and breadth in this ratio. These rectangles are said to be pleasant to look at and have been used instinctively by artists in their pictures.

The Parthenon in Athens is a temple to the goddess Athena. It is built entirely of marble, and is a fine example of Doric architecture, in which the orders or columns do not have a base. The architects used the mathematical principal of the golden section to give it proportions pleasing to the eye.

Mathematical relationship between three points, A, B, C, in a straight line, in which the ratio AC:BC equals the ratio BC:AB (about 8:13 or 1:1.618). The area of a rectangle produced by the whole line and one of the segments is equal to the square drawn on the other segment. A golden rectangle has sides in the golden mean. Considered a visually satisfying ratio, it was first constructed by the Greek mathematician Euclid and used in art and architecture, where it was given almost mystical significance by some Renaissance theorists.

The golden section was used extensively by certain painters, above all Piero della Francesca, who had an architectural background. In Vincent van Gogh's picture Mother and Child the Madonna's face fits perfectly into a golden rectangle.

In mathematics, the ratio of consecutive Fibonacci numbers tends to the golden ratio.