We have come to expect a professional standard from the layman's guides.

Interestingly, few have understood that Petrie was simply evaluating Smyth's theory in his survey of the sarcophagus in the Great Pyramid.

Smyth claimed that the external volume was precisely double the internal volume after taking into account the irregular depressions in surfaces, and that the design was a metrological standard in pyramid inches.

Petrie proved that this is not the case, not by repeating the measurements framed by the edges of the sarcophagus but by determining the mean dimensions taking into account those depressions.

In Smyth's theory, the internal volume corresponded to a sphere with a diameter equal to a quarter of the width of the chamber.

Petrie confirmed that the internal volume does indeed correspond to the proposed model, but only if the rebate for the missing lid is ignored, for which Petrie calculated that the length of the cubit would need to be 20.644 inches for a sphere with a diameter of 10/4 cubits (2.5 cubits), which Petrie regarded as close to the best determinations without actually accepting the proposition.

The internal diagonal of the sarcophagus is 112 digits and 112 x 2.5 = 280 cubits as the height of the pyramid.
The image of a sphere with a diameter of 280 cubits is latent in the north-south vertical and east-west vertical cross-sections which are each equal in area to a circle with a diameter of 280 cubits for the pi approximation 22/7 which may have been regarded as exact..

If the internal volume is doubled then this corresponds to the volume framed by the edges of the sarcophagus which was only determined by Smyth. The volume ground out of the surfaces is then the difference between Smyth's external volume and Petrie's external volume.
The smaller external volume, as determined by Petrie, corresponds to a sphere with a diameter of 22/7 cubits, so the external volume defined by the edges was the reference volume, and the true volume determined by Petrie was the symbolic volume.

Smyth claimed that a lid fitting the rebate would fit inside the sarcophagus as an internal diagonal flush with the top. I checked, then had my calculations checked on CAD, and this is so.

Smyth argued that the lid was not intended to be put in the rebate as this would spoil the design. I checked, and found that insertion of the lid in the rebate effects a geometric transition.

In 2004, I spotted the 1760 digit theory of the King's Chamber which has since been highlighted by Keith Hamilton and Dave Lightbody without mentioning me. The perimeter of the base of the pyramid is 1760 cubits. Both can be regarded as the circumference of a circle with a radius of '280'
The height of the pyramid is 280 cubits as the radius of a virtual circle, and the length of the King's Chamber is 560 digits as the diameter of a virtual circle, so the King's Chamber is a model of the pi shape of the Great Pyramid on a scale of one digit to one cubit which is a 1 to 28 scale model.

The pi theory of the King's Chamber was proposed by Smyth and accepted by Petrie, but neither spotted the scale relationship even though both were aware of cubit rods divided into 7 palms and 28 digits.

Smyth proposed his theory in pyramid inches and the theory is inevitably valid in any unit of length.

Petrie thought that cubit was divided decimally in the Fourth Dynasty, and that the digit was a separate unit of length, not a quarter of a palm, but many accepted Petrie's 22/7 pi theory from the external dimensions of the pyramids.

Of those few Egyptologists with an interest in this matter, some reject the notion that the ratio of the circumference to a diameter of a circle was of any interest to the ancient Egyptians.

Anyway, how long will it be be before someone decides my proposition on the sarcophagus is worth mentioning?

I have not published the geometric transition effected by insertion of the lid in the rebate, so anyone reading this could be the first to explain all the major dimensions of the sarcophagus.

There are, in my opinion, some deliberate anomalies, which are debateable, but the overall scheme is clear.

Similarly, in my opinion, the height of the King's Chamber, was a subtle anomaly at 319.5 digits with the base equal to 561 digits and the ceiling to 560 digits so a circuit of 1760 digits for which we can get a precise estimate of the length of the cubit.

Unfortunately, Petrie's 'measurements' hide the actual measurements again. He argued that it was necessary to deduct cracks from his measurements on the long north and south walls, but there does not appear to be a rigid connection to the east and west walls, so tenable to add back the cracks to his reported measurements.

Again, the 1760 geometric symbolism of the King's Chamber is clear from this new model, and anyone reading this could be the first to publish what it means.

Mark



Edited 2 time(s). Last edit at 04/12/2022 04:10PM by Hermione.