AE found a method to square the area of a circle from the seked as apparent from the geometric design of the Grand Gallery of the Great Pyramid.

The architect answered this question:

What is the square of the cotangent to square the area of a circle such that projecting twice the diameter onto the slope of a triangle results in a vertical rise equal to the side length of the equal area square?

The answer is D1/D2

where D1 is the diameter of a circle with a circumference of 360 digits

and D2 is the diameter of a cubit wheel equal to 28 digits

If you use this formula for any circle, say a circle with a radius of 10 cubits, you will be able to calculate the side length of its equal area square.

The answer is exact for the pi approximation 22/7.

This calculation can be reduced to a practical method by just marking off the required length on the slope of the triangle (twice the diameter of the circle) then measuring the vertical rise to determine the side length of its equal area square.

The slope of the triangle has a rise of sr55 and a run of 15, so the rise can be drawn from another triangle with a side of 3 and a hypotenuse of 8.

The triangle has a hypotenuse of sr280 (from sr55 and 15) which is why the Grand Gallery has a vertical height of sr280 cubits at the north end wall.

The average of Smyth's first three measurements taken on the sloping floor rather than the flat section is 344.6 inches.

The theoretical height for sr280 in cubits is 344.9 inches for a cubit of 20.61 inches.

Smyth proposed this was the basis of the design of the Grand Gallery, but failed to spot that the symbolic triangle defining the geometric model can be inverted to define the theoretical vertical and perpendicular heights as sr280 cubits and 15 cubits.

If you have a geometry set with a so-called set square (a right angle triangle) then just flip it over to see the geometric transformation having marked the triangle of the set square on a piece of paper. You should just aim to get a line parallel to the slope with this tool, which is the symbolic plane of the ceiling near the north end wall.

You may need to read my monograph on the Grand Gallery in order to grasp the concepts.

The Great Pyramid had a design height of 280 cubits and a circle with a diameter of 280 cubits is equal to the area of the triangular cross-section of the pyramid.

Mark

Edited 1 time(s). Last edit at 08/06/2019 12:09PM by Mark Heaton.