I tried to stress that the numbers are as seen through a modern lens to help us understand the ancient design.
One of the keys to the design of the Grand Gallery is that the seked of the Grand Gallery plus the length of the Great Step was determined as precisely 5 cubits (140 digits).
The geometric structure of the high south end defines the length of the Great Step as 93 digits x cosine of the sloping floor of the gallery.
Let's see how accurate this depiction is:
Vertical height of Grand Gallery at north end wall sr280 in cubits
Perpendicular height of Grand Gallery at north end wall = 15 cubits
Using modern maths the cosine of slope = 15/sr280 = 0.89842...
93 digits x 0.89842... = 83.367196 digits to 6 decimal places = length of Great Step using modern maths
Therefore seked of Grand Gallery is 140 digits - 83.367196 digits = 56.632805 digits
Cotangent of grand gallery is therefore 2.0226.. and tangent is 0.4944.. which corresponds to an angle of 26 degrees 18 minutes 30.22 seconds
The sloping floor of the grand gallery corresponds to the triangle latent in the soaring elevations of the gallery which has a rise of sr55 for a run of 15 cubits and a hypotenuse of sr280 cubits.
The angle of this triangle 26 degrees 18 minutes 30.24 seconds
Seked of Grand Gallery = 5 cubits minus length of Great Step
Seked of Grand Gallery = 35 palms - (93/4 palms x 15/sr280)
Seked may have been approximated as 623/44 palms which is a rise of one cubit for a run of 623/44 palms, or a rise of 28 digits for a run of 56 7/11 digits, so the approximate angle is 26 degrees 18 minutes 25.1 seconds using modern maths.
A rise of 39 cubits for a slope length of 88 cubits is 26 degrees 18 minutes 25.5 seconds.
The architect knew the seked was irregular and expressed in it the geometric design. We can see differences using modern mathematical tools.
Mark
Edited 3 time(s). Last edit at 06/09/2018 01:25PM by Mark Heaton.