The Golden Cut

Also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagram, decagon and dodecagon. It is denoted Φ, or sometimes τ (which is an abbreviation of the Greek ''tome,'' meaning ''to cut'').

To calculate the Golden Section, a distance between two points is divided so that the ratio of the longest section to the total length is exactly equal to the ratio of the shortest section to the longer section.  This ratio has the numerical value of 0.6180 and can be calculated using the formula for square roots.

The term ''golden section'' (goldene Schnitt) seems to first have been used by Martin Ohm in the 1835 2nd edition of his textbook, Die Reine Elementar-Mathematik. The first known use of this term in English is in James Sulley's 1875 article on aesthetics in the 9th edition of the Encyclopedia Britannica. The symbol Φ (''phi'') was apparently first used by Mark Barr at the beginning of the 20th century in commemoration of the Greek sculptor Phidias (ca. 490-430 BC), who a number of art historians claim made extensive use of the golden ratio in his works.

Throughout history, artists and philosophers have been fascinated by the Divine Proportion, as it can be applied both to the smallest of units (cells, atoms, molecules, quarks) and to the largest of units (solar systems, galaxies, the universe).  Humans naturally feel attracted to works which have been constructed using the Divine Proportion, although modern science has yet to find a measurable, quantifiable explanation as to why some works are simply more “appreciable” than others.