PENTAGON AND THE GOLDEN RATIO

by Nikhat Parveen, UGA

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 insignia.

Pentagon, 5 five pointed star

*Click here for
the GSP file of Pentagon*

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.

Michelangelo's *Holy Family* ... and
Raphael Crucification are other examples,
wherein the principle figure outlines the Golden triangle which can be used to
locate one of its underlying pentagrams.

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