Many have posted on the topic. I thought I might ask a few questions.

Seked; run to rise provides slope.

In regards to G1, since that seems to be a well documented example of Seked employ, I find it curious that this slope often provided only occurs from the midpoint of any base side to the top, only account for the face slope.

for a right triangle, to measure the angle/slope of its hypotenuse a seked is employed via palms (run) to 1 cubit (rise).

for the sake of simplicity lets assume G1's base side lengths are all the same at 440 cubits and its apex is 280 cubits high.

from the midpoint of any side of G1 you get the seked 5 1/2 (5 palms 2 digits) for the face slope.

However as you move to a point along the base from the midpoint, say 10 cubits south of the western base side, the triangle formed by this new point and the pyramid apex will have a different Seked.

Because the base (finished) was square as you move to a base corner from the midpoint of a side the Seked changes dramatically, the corner provides a Seked of 7 palms 1 digit.

the difference in slope of the face (midpoint) and corner respective is 51.89 to 42.09 or roughly 10 degrees.

Thus in the minds of the builders these slopes represent the finished product they set out to build.

moreover, I have been mentioning only the casing in finished form, as we know the core masonry (blocks of stone stacked in increments to accommodate the varied slopes found in the structure) reveal a much different Seked than the 5 1/2 because at the midpoint of each side this point is purposely indented by a noticeable degree. Just because its the core, absolute an engineering marvel in and of itself, the Seked had to be determined to receive the facing stones.

My point in bringing all of this up is the geometry employed to achieve the G1 construct was very sophisticated and advanced.

Interesting that the Babylonians approached trigonometry with an ingenious method of finding ratios (Plimpton 322, cuniform tablet circa 1800 BCE) which was extremely accurate. Instead of using a circle to measure angles like we moderns do, they employed right triangles found in rectangles or squares...a quadrant method to express ratios, I wonder if the Egyptians employed the same ratio method with the Seked to measure compound slopes. Not sure if anyone has attempt to correlate the two systems but thought it would make a topic to discuss.

All the best,

B.A.Hokom