golden section

golden section. Also called the golden cut or mean, or harmonic proportional ratio, it may have originated in C6 bc in the circle of Pythagoras, was certainly known during the time of Euclid (c.325–c.250 bc), and was held to be divine by several Renaissance theorists, especially Luca Pacioli (c.1445–c.1514) in his De Divina Proportione, written in 1497 and published in Venice in 1509. It can be expressed as a a straight line (or as a rectangle) divided into into two parts so that the ratio of the shorter part (a) to the longer (b) is the same as the ratio of the longer (b) to the sum of the shorter and longer parts, or a:b = b:a + b, or that the ratio of the smaller part is to the longer as the latter is to the whole. The ratio is expressed in algebra as Φ (Phi, the first letter of the name of the Greek sculptor Phidias, or Pheidias (c.490–430 bc) ) = (1 +√5)/2, which comes to 1.61803. Thus the ratio is approximately 8: 13.

Bibliography

Borrisavlievitch (1970);
Ghyka (1976);
Hagenmaier (1977);
Huntley (1970)