Hello Dave

Whether one dismisses it as coincidence or whatever, it is undeniable that the base perimeter of the Great Pyramid is related to its height as the circumference of a circle is related to its radius. I think it is also striking that if we take the apothem or slope length of the Great Pyramid as the radius of a circle (356.09 cubits) then using 22/7 for pi the circumference equals 2238.28 cubits. This is the hypotenuse of a 1417.50 x 1732.22 right triangle, which so happens to define the overall layout of the Giza site in John Legon's interpretation of Petrie's data. Incidentally a circle whose radius equals the height of the GP plus the apothem has a diameter of 1272.18 cubits, 1000 x sqrt phi. A circle whose radius equals the height of the GP plus the semi-base will have a circumference 1000 x 22/7 cubits. Taking the perimeter of the triangle which defines the GP slope (220+280+356.09 = 856.09 cubits) as the radius of a circle then using 22/7 the circumference shall be 5381.14 cubits. This equals 1731.14 + 1414 + 2236 cubits, only a cubit or so out from the perimeter of a true square root triangle.

To summarize:

GP height = radius then circumference = GP base perimeter
GP apothem = radius then circumference = hypotenuse of 1417.50 x 1732.22 cubit right triangle
GP height + apothem = radius then diameter = 1272.18 cubits
GP height + semi-base = radius then circumference = 3142.86 cubits
GP height + apothem + semi-base = radius then circumference = 1731.14 + 1414 + 2236 cubits

Remarkably if we convert the perimeter of a 1417.50 - 1732.22 - 2238.28 triangle from royal cubits to the shorter "common" cubit which is 6/7 of the royal, we get:

5388/6 x 7 = 6286 or 2000 x 22/7 (99.99%)

This is the circumference of a "unit" circle with radius 1000 common cubits. Since John Legon derives the Giza site plan from a unit square of width 1000 royal cubits you could say we have now come "full circle."

Regards
Nick



Edited 1 time(s). Last edit at 01/13/2012 11:03AM by affiliator.