David:
Let me try and explain what error you have posted...it's called double assumption.
First:
You present a height as quoted/calculated by an “Egyptologist of renown”...!
Second...you use his measure and explain that the pi ratio that I present is incorrect, without giving the problem a second thought.
The error:
The calculated height of the structure uses the base angle of the pyramid and the individual who measured this angle must be claiming it different than Petrie’s.
The solution is resolved this way.
a) "If" the base angle was intentionally designed having a 4/pi ratio (28:22) seked then the height would be (2/pi times the total base width).
b) "If" the height of the pyramid was designed to be pi (22:7) times higher than the Grand Gallery ceiling then the ceiling has to be (2/pi times the total base width)/(22/7) long...or 0.2026 times the base length.
The base is 9067.7 inches (viewing the structure from the east).
Therefore the length of the ceiling should be (9067.7 x 0.206) = 1837.5 inches.
Now Petrie didn't realize the importance of what he was measuring, but he meticulously measured the length of the Gallery and his calculations are in print...1838.6 inches (he excluding a tolerance in measure).
“…From this the length of the roof of the gallery is 1688.9-40.45 = 1648.4 horizontal, or 1838.6 sloping…”
The error, using a ten-decimal place calculator, is 1.1 inches...or 0.0006:1 or .06%...or far more accurate than you first assumed...the Egyptologist you quoted may be in error...definitely not the pyramid builders.
Best.
Clive
a function of the base angle proposed.