You wrote: Well, that's brave of you to volunteer that the pyramids are so hard to measure that they're not going to support anyone's premises including your own, lol - and I do agree, everyone's measurements describe the GP as having unequal sides but the troubling thing is that no two may agree what the longest or shortest sides are.
By far the largest obstruction to understanding Ancient Egyptian Pyramids are assumptions. The most common is made by people never having been involved in building construction or the trades, is the assumption Petrie’s or anyone else's measurement are the intended values of the Ancient Egyptian builders. In assuming the measurements to be the intended leaves no room for the building errors. Those are the inevitable errors which always creep in to a building the scope and magnitude of G1. Coupled with a lack of a clear understanding, especially the purpose and fixed length of the cubit, along with the methods of the Ancient Egyptians. Makes assuming Petrie’s or any other surveys values to be those intended by the Ancient Egyptians a precipitous endeavor and only introduces additional errors. In the real world can the most tedious of surveys on a structure the age and condition of G1 ever be considered anything more than guidelines? No disrespect towards W. F. Petrie, or any of the other surveyors intended, since they did a superb job of surveying the Pyramids. This conundrum is exacerbated even further by the lack of a consistent or uniform length for the original Royal Egyptian Cubit. Then there is always the possibility the Ancient Egyptians could not measure as accurately as many assume they could. The first question that comes to mind is: Based on what benchmark measurements do we make the assumption?
Due to the limitations of their system of unit fractions only make rational numbers. If they were to calculate the hypotenuse of a square their solution for the √2 would be 1 + 1/3 + 1/33 + 1/36 + 1/44 Which equals G1 seked rise run of 14/11 x (10 + 1/9) the rise and run of the hip formed by the sides of the pyramid at the corners = 140/99 a difference of 0.000072148 from our current value for √2.
√3 = 1 + 1/3 + 1/4 + 1/8 + 1/42 = 97/56. Where the difference is 0.0000920958 between 97/56 and our current value for √3.
Being there is no proof they calculated the square root 2 or three the above is only speculation. It is possible when setting the square of a building they employed the 3 4 5, or 6, 8, 10, triangle at the corners, as we did in the field when laying out buildings.
You wrote: We can say the AEs had no idea what the modern foot was
You could say that, but I wouldn't bet any great sum of money on that assessment, it could be wrong. Remens and Royal Cubits are, mathematically when expressed in cubits palms or digits. 1 cubit 7 palms' 28 digits for the cubit and 5 palms, 20 digits where the Remen is 1/2 + 1/7 + 1/14 of one cubit, so Remen is 5/7 cubit the Ancient Egyptian foot is 4 palms, 16 digits equal to 4/7 of a cubit.
You wrote: That pyramidion height and 10 Royal Cubit ratio is locked in by that.
Now I could be wrong, but I believe the current width of the platform at the top of the G1 is somewhere in the neighborhood 44 feet or 528 inches. So how many courses must be replaced to achieve that 10 cubit dimension?
It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with
Change of experiment to evidence mine