We can draw a triangle with a rise of 320 digits and a slope length of 720 digits from the point the virtual projection of the floor of the gallery strikes the south end wall of the gallery. This triangle marks the junction of the ceiling and south wall of the King's Chamber. The horizontal displacement is 645 digits.

Here's a summary of key levels:

Remarkably, I found that the top of the lowest overlap on the north end wall is at the level where the square of the rising pyramid has a side length of 365 cubits, accurate to a small fraction of a digit.

In my model the foot of the gallery is at 1156 digits above the base.

I found that there is an exact parallelogram defined by the Queen's Chamber and the Grand Gallery.

Point A is on the base of the pyramid 1156 digits below the foot of the Grand Gallery

Point B is the foot of the Grand Gallery

Point C is a projection of the floor of the Grand Gallery on to the south end wall at a level of 2,289 digits, which is exactly 7 digits below 82 cubits as the half area level of the pyramid.

Point D is 1156 digits below point C on the floor of the Queen's Chamber at a level of 1133 digits above the base square.

A number of years ago I published a model of the Queen's Chamber on the internet and proposed a foundation level of 1129.5 digits above the base square, but a floor level of 1133 digits.

The original floor is missing but I took as 7/2 digits as half the depth of the King's Chamber floor which is 7 digits as the difference between the bottom course of the granite blocks and the actual floor level.

The floor level of the King's Chamber is therefore at 2289 digits + 7 digits = 2,296 digits.

In my model the half-height of the east wall of the Queen's Chamber is at a level defined by the half-height of the pyramid with the ceiling of the King's Chamber exactly in between.

All these theories now yield an exact parallelogram, mentioned here only to say your projection of 29 cubits sounds interesting, but let's check it out.

I have the height of the King's Chamber ceiling as 2,296 digits + 313 digits above the base square which is 2,609 digits.

For your model to fit my models the projection must rise 320 digits from the south wall of the gallery to the south wall of the King's Chamber at the level of the ceiling.

The Grand Gallery has a symbolic rise of sr55 cubits for a run of 15 cubits so this requires a horizontal distance of 320 digits x 15/sr55 = 647.23 digits or 23.11 cubits from the south wall of the gallery to the south wall of the King's Chamber.

It is 268.9 inches (330.6 - 61.7) to the north wall which is 13.047 cubits or 365.31 digits, which I think was intended to be 365 digits (268.7 inches).

365 digits and 365 cubits may be linked to the number of days in a year.

The intended distance to the south wall of the King's Chamber appears to be 280 digits (10 cubits) plus 365 digits which is 645 digits (23 cubits and 1 digit)

In theory the projection would strike the south wall at 318.9 digits above the bottom of the lowest course of granite blocks, or 1.1 digits below the point indicated on your sketch.

The theoretical slope of the gallery to square the circle is 26 degrees 18 minutes 30 seconds for the pi approximation 22/7.

Alternatively, the sine of 26 degrees 18 minutes 25.45 seconds is 39/88 corresponding to the vertical rise / slope length of gallery.

The projection beyond the Great Step to the south wall of the gallery has a length of precisely 93 digits, thereby defining the length of the Great Step as an irregular 83.37 digits. (Theoretical length of step 61.36 inches for 20.61 inches per cubit).

The projection beyond the gallery rises 318.9 digits for a run of 645 digits so the slope length is an irregular 719.5 digits plus 93 digits to the south wall of the gallery is a total of 812.5 digits. This is 29 cubits and half a digit.

We can, however, draw a triangle with a rise of 320 digits (height of King's Chamber as 5 courses of 64 digits) and a slope length of 720 digits from the point the virtual projection of the floor of the gallery strikes the south end wall of the gallery. This triangle marks the junction of the ceiling and south wall of the King's Chamber most precisely so. The horizontal displacement is 645 digits, as above. within 1/50 of a digit.


Mark