RE BENT PYRAMID:
Petrie's mean side length is 7459.0 inches corresponding to a cubit of 20.719 inches assuming a design length of 360 cubits, or 20.605 inches assuming a design length of 362 cubits.
Dorner's mean side length is 7465.0 inches corresponding to a cubit of 20.736 inches assuming a design length of 360 cubits, or 20.622 inches assuming a design length of 362 cubits.
Petrie only determined the length of three of the four sides, and for two of those sides Dorner determined a similar length so we should take those sides as the most reliable indication of the intended side length.
(North side plus west side)/2 = 7461.75 inches for Petrie and 7,460.25 inches for Dorner with a mean of 7461.0 inches which corresponds to design length of 360 cubits for a cubit of 20.725 inches, or a design length of 362 cubits for a cubit of 20.610 inches.
It seems obvious that both surveyors measured the same dimensions, and it seems to me that Petrie marked PAVE at one side of the casing stone and MENT at the other side of the casing stone with the top edges at the same level so both surveyors actually measured the lengths formed by the intersection of the sloping faces of the pyramid with the top edge of the PAVE.
Quote from Alex just posted:
The casing has hidden bottom edge in the corners only. Along the sides casing blocks lie on the single foundation blocks (see Fig.1 No.10) the upper planes of which are at the same level with the pavement.
This also means that the true side length to common observation (and to builders who were aware of the MENT) was where the top edge of the PAVE intersected with the face of the pyramid, so the bottom of the PAVE is irrelevant unless it can be shown that it had a precise uniform depth all around the pyramid against the sloping edge of the casing stone such that the pyramid has a concealed square perimeter at the bottom of the PAVE, but the post from Alex clarifies that such casing stones do not exist, so there is only a hypothetical virtual square projected by the corners.
The notion of a concealed and projected virtual square perimeter cannot reconcile models of 360 and 362 cubits unless the top edge of the PAVE is 10 palms above the bottom edge of the PAVE in the corners. The thickness of the PAVE beyond the casing stones looks far less than 10 palms, but whatever its depth the notional concealed square would be even longer than 7459 inches which has been ascribed an intended length of 360 cubits according to Petrie and 362 cubits according to Dorner, so something longer than 362 cubits in the case of the latter.
In reality there is no significant difference between the surveys of Petrie and Dorner for the purpose of determining the size of the base square of the Bent Pyramid.
From Petrie's Inductive Metrology 1877 and the debate over the size of the Great Pyramid, Petrie had to conclude that the true base side length was the intersection with the top of the PAVE for which he had then to suggest a reasonable intended dimension.
Robin Cook takes Dorner's view of 362 cubits, and supports it with an ingenious geometric model yielding a cubit similar to that of the Great Pyramid.
I took Petrie's view that the length of the cubit did change slightly, but some hold the view that 20.7 inches is so much longer than 20.6 inches that they can't accept a change of 0.1 inches in a generation.
I got a model of a 360 circle in the design of the Bent Pyramid complex from 20.7 inches.
THE RED PYRAMID
Anyone taking 362 cubits as the intended length of the Bent Pyramid should seek to evaluate the Red Pyramid with a cubit of 20.61 inches for both the internal and external dimensions, and then present us with a model where three pyramids, built one after another, all conform to a cubit with precisely the same length, including the Great Pyramid.
On the contrary, I am free to find a solution to the design of the Red Pyramid assuming the cubit of the interior is the same as the cubit of the exterior plus or minus say 0.01 inches analogous to the Great Pyramid where Petrie's cubit of 20.62 inches appears to be 20.61 inches from the base square and 20.63 inches from the King's Chamber. Moreover, the King's Chamber is a model of the exterior of the Great Pyramid.
The Red Pyramid was built before the Great Pyramid with its 22/7 symbolism, but after the Bent Pyramid with its 360 symbolism, so I put the two together and found a model of the exterior latent in the interior which is consistent with Petrie's survey of the first antechamber and Dorrner's survey of the size and shape of the Red Pyramid from its base side length and slope.
Today I borrowed a copy of John Romer's book on the Great Pyramid having been told that it contains a reference to Dorner's survey of the Red Pyramid which is indeed reported as having a side length of 219.08 metres at the base.
Dorner's surveys of the Great Pyramid and the Bent Pyramid yield the same dimensions as Petrie for practical purposes, so I think we can have confidence in Joseph Dorner.
Dorner's angle for the Red Pyramid, quoted on this thread, is 44 degrees 44 minutes, which is so very close to my theoretical slope of the cotangent of 100/99 having decided on this angle without the benefit of Dorner's angle.
As things stand perhaps Robin Cook's elegant model of the Bent Pyramid has been the front runner on this forum for some years.
I think my model of the Red Pyramid bears out the intended design of the Bent Pyramid, as shared with this forum 10 years ago (with diagrams on my website), but the purpose of my current investigation, started two weeks ago, is to determine the design of the Red Pyramid, not to disprove Robin Cook's model of the Bent Pyramid.
At present I just want to be sure of what Dorner actually reported, especially as others may argue that Dorner actually reported something quite different from values quoted by others.
I am hoping that there is no way Dorner's survey can be manipulated, or any way others can create uncertainty.
Do we know Dorner's measurements of each side of the Red Pyramid?
Do we know if Dorner measured a lot of angles in arriving at 44 degrees 44 minutes?
Are Dorner's diagrams of the Red Pyramid available?
Mark
Edited 7 time(s). Last edit at 02/25/2020 06:40PM by Mark Heaton.