Thursday, September 27, 2007

The amazing Golden Ratio

Al Ahram Weekly (Assem Deif)

Historians trace the Golden Ratio back to Euclid, yet it appears that even before him it was governing the dimensions of monuments in ancient Egypt. The most pronounced of these is the Great Pyramid. The dimensions of the inner triangle (the so-called "Egyptian triangle") of Khufu's Pyramid, for instance, in Royal cubits (one cubit equalling roughly 0.524 metres), are (220c, 280c, 356c) i.e. in the ratios 1 : sqrt(Phi) : Phi. That the foregoing relation is not a matter of coincidence is discussed elsewhere. However, the Great Pyramid is not the only structure from ancient Egypt that complies with constants like Pi or Phi; Schwaller De Lubicz, who studied the temples of Upper Egypt from 1937 to 1952, collected massive amounts of evidence to show that the Egyptians used the Golden Ratio in many ways both in the architecture of their temples and in their drawings. So whereas, prior to De Lubicz's research, the discovery of the "golden rule" was generally credited to the Greeks (although some historians denied this), the findings of such Egyptologists as De Lubicz and Fliders Petrie produced irrefutable proof that the Egyptians had a mathematical understanding of these constants, the ratios, not the symbol, 1000 earlier. Petrie, for example, noticed that the dimensions of many Egyptian tombs, especially those of a parallelepiped structure, adhered to the ratios 1 : Phi : Phi square. The same ratio also appears in a grid surrounding a human body depicted in the royal tomb of Amenhotep III in the Valley of the Kings.

See the above page for the full story.

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