Auream quisquis mediocritatem diligit, tutus caret obsoleti sordibus tecti, caret invidenda, sobrius aula. (He who chooses the golden mean safely avoids both the hovel and the palace).
A mathematical ratio in which width is to length as length is to length plus width This ratio has been employed in design since the ancient Greeks It can also be found in natural forms
(aka 'golden section' or the French 'Section d'Or') The golden section was developed as early as by Euclid and is supposed to refer to a proportion that is irrational and is thought to have its own intrinsic value, the value being at one with the universe itself The actual definition of golden section is a line that is divided so that the smaller part of the line is to the larger part of the line as the larger part is to the whole line This usually turns out to be 8: 13 and is visible in most works of art
(or ratio) The positive solution to the quadratic equation, x^2 + x - 1 = 0, which is (-1+sqrt(5))/2, or approximately 618 This has the proportionality property: x: 1 = (1-x): x, which defines the placements of evaluations for the golden section search More information about the golden mean is given at the Favorite Mathematical Constants site