Yes

The sloping faces of Khafre's pyramid conform to a rise of 4 for a run of 3 so a slope length of 5 which is the triplet you mention.

I think this is an important feature of the design, but first let's look at a simple proposition:.

It is proposed that the peaked roof of the burial chamber was designed to to have an area of 274 square cubits as the architect’s signature on the pyramid's design height of 274 cubits.

The rectilinear section of the burial chamber was cut out of the bedrock so there would have been a risk of removing too much bedrock which could not have been replaced if a mistake had been made. The rectangular floor ‘27 x 9½’ has appeared to be the nominal product of an ample excavation, but it is now proposed that the chamber was hewn out of the bedrock with remarkable skill pursuant to a geometric design.

The roof of the burial chamber may have an intended slope corresponding to a rise of 1 cubit of 7 palms for a run of 19 palms so potentially a ratio of ‘19 to 1’ regarded as palms to cubits. On this basis the ridge of the roof should be ‘7/19 x 1/4 x 19’ cubits above the level of the top corners because half the width of the chamber is ‘1/4 x 19’ cubits. As such the peak would be 36.1 inches (0.917 metres) above the top corners as ‘7 x 1/4’ cubits for a cubit of 20.62 inches (0.5237 metres). Petrie cited a measurement of 36 inches (0.914 metres) taken over forty years previously in the early nineteenth century. This requires confirmation or otherwise by way of another survey.

At first sight the area of the roof appears to be approximately 270 square cubits (two sections x 27 cubits x 5 cubits).

If the intended area was 274 square cubits then the length of chamber would need to be ‘7 x 1/4’ digits longer (+ 1.29 inches or + 32.8 millimetres) if the peak of the burial chamber had a design height of ‘7 x 1/4' cubits above the top corners.

The length of the chamber is 0.91 inches (23.1 millimetres) longer than expected length of 556.74 inches from an evaluation of Petrie’s measurements for a cubit of 20.62 inches, so potentially a subtle feature of the design.

The architect may have relied on precise measurement to determine the hypotenuse, but we can calculate using 'Pythagoras'.
The right-angled triangle of the roof section or gable has a proposed intended height of 1.75 cubits as the vertical and 4.75 cubits as the horizontal (half the width of chamber 19/4 cubits)
Therefore, the area of half the roof is the hypotenuse multiplied by the length of the chamber.

Proposed area of half of roof is precisely 137 square cubits as:
length (27 cubits + 7/4 digits) x hypotenuse (square root of the sum of the squares of 4.75 cubits and 7/4 cubits)

This rather elegant construction of numbers is accurate to better than 0.01 square cubits.

Proposed symbolic area of roof of burial chamber = 2 sections of 137 square cubits = 274 square cubits

Proposed design height of pyramid = 274 cubits

This model may have been on the drawing board by way of an ingenious construction of numbers so potentially without the need to order the masons to execute a trivial extension of 1 part in 432 on a length of 27 cubits to 27 cubits plus 7/4 digits (27.0625 cubits because there were 28 digits in a cubit).

Such a tiny refinement would not have been meaningful unless the architect was sure that a much higher build standard than 1 part in 432 could be achieved. Other dimensions such as the breadth of the chamber and the base square have a much higher builder standard on the basis of conformity to a cubit of 20.62 inches, but this does not necessarily mean that the architect was absolutely sure that such a precision had been achieved, so perhaps there was a need to lock in the design in a novel way, or alternatively a belt and braces approach.

Mark



Edited 4 time(s). Last edit at 04/27/2021 03:00AM by Mark Heaton.