Here is an equation for the 20 million cubic inches:
Length - 20 cubits
Width - 10 cubits
Height - 11.4159... (with perimeter of long walls as circumference of circle with diameter = length)
i.e. length 20 cubits so perimeter 20pi cubits. 20 + 11.4159 = 10pi, x 2 = 20pi
So the equation is:
solving for the length of the royal cubit as y
20y x 10y x 11.4159y = 20,000,000 cubic inches
20 x 10 x 11.4159 x (y cubed) = 20,000,000 ci
20 x 10 x 11.4159... = 2283.185...
20,000,000/2283.185... = 8759.6919...
cube root of 8759.6919... = y
y = 20.61403... = length of royal cubit
This is the royal cubit proposed by de Lubicz = pi/6 of a meter.
20.61403... x 6/pi = 39.36990... inches
modern meter = 39.37000 modern inches
So interesting connections between royal cubit, meters, inches and pi.
de Lubicz thought pi/6 = phi sq/5 was significant, and since phi derived from sq rt 5 (de lubicz thought sq rt 5 and 5 and much else derived from phi rather than the other way around) maybe phi implicated in dimensions from base to ceiling also...
half of the volume of the KC, with a square base of 10 cubits and the same height as the KC (10pi - 20)
you get 10,000,000 cubic inches with basically all of the same relationships.
I was just looking around to see where the 20M cubic inches might have been mentioned before and in the postscript to Inheritance by Piazzi Symth, James Simpson mentions this in his letter. He also says the QC volume is 10M cubic inches. If we take the baselengths of the QC as 10 and 11 cubits, and use the same 20.61403 length that we got from the KC, then:
10 x 11 x (20.61403 sq) = 46742.205
10,000,000/46742.205 = 213.9348...inches for the height.
Petrie gives 184.47 for the height to the top of the north and south walls, and he gives 245.1 for the height of the chamber from the base to the apex in the middle of the east and west walls. Since the height from 184.47 to the apex is triangular, rising to a point at the apex, the volume is half of the triangular height of 184.47 to 245.1:
245.1 - 184.47 = 60.4
60.4/2 = 30.2
184.47 + 30.2 = 214.6 inches for the height (adjusted for 1/2 of the tapering part).
This is within one inch of the calculated height of 213.9 inches needed for 10M cubic inches, and keep in mind that Petrie acknowledged that the floor of the QC was unfinished and irregular and he was giving his best estimate of the floor level under the circumstances, so Simpson's claim of 10M cubic inches for the QC, or 1/2 of the KC, seems reasonable.
I realize that the 20M figure you mentioned was not the point of your post except as it might offer support for the 1/43,200 ratio, but I either had not seen or had forgotten the 20M cubic inch figure and it caught my attention
Edited 5 time(s). Last edit at 24-Dec-19 09:35 by Jim Alison.