Egyptian Architecture

The ancient Egyptians used the golden ratio in much of their artwork, including in heiroglyphs, the pyramids, and many statues.

The Ahmes papyrus of Egypt gives an account of the building of the Great Pyramid of Giza in 4700 B.C. with proportions according to a "sacred ratio."  Modern measurements show that the ratio of the distance from groud center to base edge, to slant edge of the pyramid is amost exactly 0.618. The sides of the pyramid appear to be golden triangles.  A golden triangle is an isosceles triangle with base angles of 72� and a vertex angle of 36�.

The picture above shows that the apothem (central height) of any of the side triangles of the pyramid relate to half the base in the proportional ratio of the golden section.  In cubits (the measurement used by ancient Egyptians): 1/2 base = 220; apothem = 356; 356:220 = 1.618

Also, the 3-4-5 triangle is the golden ratio between its 5 unit side and 3 unit base.   The Egyptians thought this was of vital importance.  They used this triangle in many ways, such as a surveying tool and in the pyramids.

The three oldest Giza pyramids lay on a Fibonacci spiral and the opening to the Hall of Records is geometrically marked by the lines which bisect the golden rectangle.

The opening to the Halls of Records, which hold the history of the Earth, is found in the right shoulder of the Sphinx.  This has been clearly marked geometrically. Looking at the picture above, if the golden  rectangle that fits around the spiral at the Giza plateau is bisected it passes exactly through the headdress of the Sphinx. Also, a line extended from the southern face of the middle pyramid and the line that bisects the golden rectangle form a cross that marks a significant spot on the right shoulder of the Sphinx.

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