The Pentagon

The pentagon is a 5 sided figure (Penta meaning 5.) It is seen in the painting as the surface of the dodecahedron which is one of the Platonic solids. The famous building, the pentagon which is the seat of government in the USA is built in this shape. Inscribed within is the 5-pointed star, a pentagram, frequently seen in military ensignia. Superimposed on this pentagram is a golden proportion gauge showing a smaller to larger division of the Golden Proportion on a line (a chord) of the pentagon as seen below.


Pentagon, 5 Pointed Star


The ancient Greeks, starting with Pythagoras in about 550 BCE, were very interested in the way the the diagonals of the pentagram (the 5 pointed star) intersect each other in the golden proportion and gave the first formulation of the golden proportion in the following terms.

" The diagonals of the pentagram cut each other in division of extreme and mean ratio"
This latter expression is the inspired title of a book by Roger Hertz-Fischler printed in 1987 in which he traces the history of the Golden Proportion in great detail. The book ranges from ancient Greece across the globe, embracing many different cultures and, from the time of Pythagoras, to the modern day.
Huntley in his book The Divine Proportion [Dover 1970] describes the reverence which the ancient Greeks felt for the Golden Proportion as symbolized in the Pentagram. They felt that it had a mystical significance and revered the pentagram as the symbol of their secret society. The Pythagoreans were both fascinated and perplexed by the intersecting cords of the Pentagon giving a double Golden Mean Proportion, details of which are described under, "what's special".