The Golden Thread

The mathematics of Euclid's Elements is a large collection of relatively difficult material, splendidly organized, and formally presented. Among its 700 or so propositions are a relatively small number of constructions. The theorems end with "Q. E. D." meaning "that which was to have been proven." The constructions end with "Q. E. F." meaning "that which was to have been done."

After devoting an hour or so every morning to mathematical meditation on Euclid over the past year or so, I developed the idea that these constructions comprise the target and goal of all of Euclid's work. Seen by themselves, a clear thread emerges: a step-by-step construction of the five Platonic solids, the subject of the last three books of Euclid. The main milestone is achieved in Book VI, with the construction of the pentagram, or pentagon, in a given circle. In this difficult task, the key step is the "DEMR", Division into Extreme and Mean Ratio, or "golden section."

The Golden Thread will be the story of the golden section, from Cheop's pyramid to the present. This is a tale of sacred geometry and secret knowledge, of alchemy and astrology, of stone masons, sculptors, and musicians.


Revised Sun 28 January 1996.