Thanks for the commendation, but I know you need to know which bunker I am in order to blast me out of it.

As you can read I have just replied to Pistol, but I have my ammunition at the ready with a mass of words to copy and paste.

The design of the sarcophagus includes a miniature model of itself as a model of the size and shape of the Great Pyramid as apparent from the square rebate which has a side-length of 20/9 digits. Smyth proposed that the internal space corresponded to a sphere with a diameter equal to a quarter of the width of the chamber (2.5 cubits). Petrie could not fault the theory. Smyth also proposed that the external volume was double the volume of the sphere, but Petrie argued that it was not by taking into account the slight irregular depressions on the external surfaces.

The Coffer has a nearly square rebate with width and depth of 20/9 digits, and I propose that the design was a square rebate with the slight undercutting for security.

The rebates of the north and south ends of the sarcophagus intersect the rebate of the east side such that there are two virtual cubes in the corners, as in any square rebate, so the notion of doubling the volume of a cube is an inevitable feature of the design. In this particular case the virtual cubes are in the NE and SE corners of the sarcophagus. There are no similar cubes at the west end of the sarcophagus because the rebate on the west side is equal to the thickness of the west side in order to accommodate the sliding lid.

In the proposed design the upright vertical sections of the pyramid on the N/S and E/W axes have circles equal to the triangular cross-section of the pyramid thereby projecting a sphere equal to the height of the pyramid. Analogous upright vertical sections of the virtual cubes in the NE and SE corners of the sarcophagus divide these cubes in to 8 smaller cubes, with the sections aligned to the N/S and E/W axes. This model highlights that doubling the side length of the cube increases the volume of the cube by 8 times. The square of the rebate has analogous equal area circles on each of N/S and E/W axes thereby projecting spheres in the NE and SE corners of the rebate.

In the Rhind Mathematical Papyrus the area of a square is equal to the area of a circle with the side length of the square taken as 8/9 times the diameter. It follows that the diameter of the circle is equal to 9/8 times the side length of the square. The square rebate has a side length of 20/9 digits so the virtual circles on the N/S and E/W axes in each corner of the rebate are equal to the area of a circle with a diameter of 2½ digits (20/9 x 9/8 = 20/8 digits).

It is now apparent that design projects a sphere with a diameter of 2½ digits in each of the corners of the rebate. This miniature model captures the model of doubling the volume of the sphere with a diameter of 2½ cubits because there are 2 spheres, and the external volume of the sarcophagus is double the internal volume in the proposed design.

The miniature model spheres are obviously on a scale of 1 digit to 1 cubit. The internal diagonal of the sarcophagus is 112 digits so the full scale representation of the model sphere with a diameter of 2½ cubits is a sphere with a diameter of 280 cubits (112 x 2½ cubits).

The sarcophagus is a model of 2 spheres because the internal volume is equal to the volume of a sphere with a diameter of 2½ cubits and the external volume is equal to the volume of 2 spheres with a diameter of 2½ cubits. Likewise the miniature model has 2 spheres with a diameter of 2½ digits. It follows that we may consider 2 spheres projected on to the pole of the pyramid.

One of these full scale spheres may be regarded as sitting on the base of the pyramid, and thereby defining the size and shape of the pyramid on the N/S and E/W axes. The other sphere may be regarded as a projection of the King’s Chamber because the sarcophagus sits on the floor of the King’s Chamber.

It turns out that the plane of the floor of the King’s Chamber is at a level of 82 cubits above the base and thereby divides the pyramid triangle into 2 equal areas. It is as if the floor level of the King’s Chamber divides the circle equal to triangular cross-section into 2 semi-circles.

Therefore a full scale sphere with a diameter of 280 cubits may be regarded as divided into 2 hemispheres by the plane of the floor of the King’s Chamber. If each of these circles is assigned a relative volume of 1 then the sphere has a relative volume of 2, so the relative volume of the pyramid is 22/7.

You can see and understand all this at a glance if you understand what you are looking at.

Mark

Edited 2 time(s). Last edit at 08/19/2018 11:53AM by Mark Heaton.