Several of the posts on this thread have expressed the opinion that there is no evidence of any basis other than sekeds in the dimensions of the pyramids. I believe that the presence of the golden section in many of the dimensions of the great pyramid is evidence of the intentional incorporation of phi as a basis for the dimensions of the pyramids.

I believe the presence of the phi proportion in the overall dimensions of the pyramid (slant height divided by half base) is evidence of intention. I also believe that the statement by Herodotus supports this conclusion. He said the side was 8 plethra and the height was the same. The plethra was a meaure of length of 100 greek feet and also a measure of area of an acre of 100 x 100 greek feet. The area of each of the sides of the pyramid is equal to the half base times the slant height (220 x 356 = 78320 square cubits) The area of the height squared is 280 x 280 = 78400 square cubits. This is a near equality that is within the margins of error of our measurements of the sidelengths and the height of the pyramid. On the other hand, the side length is nowhere near the same has the linear height of the pyramid. This is why I think it is clear that Herodotus was refering to square measures of plethra in his description and this is why I think it is wrong to insist that Herodotus was referring to linear measures and he was just way off, when his statement that the sides and the height are equal is correct. using the area measure definition for plethra. The half base (or short side of a right triangle) times the slant height (or hypotenuse of a right triangle) being equal to the height (long side of a right triangle) squared, is the classic definition of the unique phi triangle known today as the Kepler triangle because of his description, which is the same as Herodotus description of the great pyramid.

Despite this, it has been argued that the phi proportion in the diemensions of the pyramid is no evidence of it's intentional use because the phi proportion could just be an artifact of a 14/11 or 5.5 seked slope.

I also believe that the presence of the phi proportion in the king's chamber is evidence of intention. The height of the king's chamber from the top of the flooring blocks to the ceiling is 11.18 cubits. This precise measure is apparent when the height is calculated based on the height of the five courses of the walls of the chamber, which are 16 palms, or 64 fingers each, minus the 1/4 cubit height of the flooring blocks above the base of the first course of the walls. The height of the five courses of the walls and the height of the flooring blocks above the base of the first course is clearly and preciesly established by the survey data. The unusual height of 11.18 cubits, is an exact expression of the phi factor of the square root of five times five.

Despite this, it has been argued that since the floor is a 20 x 10 rectangle, the diagonal length is equal to the square root of five times ten, so the height of the chamber may just be an artifact of the builders setting the height at one half of the diagonal of the floor for no reason having to do with the phi function of both measures. I might add that if this explanation is correct, it is at least evidence of an awareness of the diagonal of right triangles, which has also been denied by some.

However, having thought about it and having read all of the 150 plus posts on this thread, I know of no alternative explanation for why the descending passage would have been placed in such a way as to be divided into a golden section by ground level, other than the obvious explanation that it was intended. To achieve this result, the slope of the passage, and it's length, and the height of the entrance above ground level all had to be precisely coordinated. I understand that the slope of 2/1 can serve as it's own explanation (fractional seked 3.5). I also understand that the approximate length of 200 cubits for the passage has been suggested as an explanation for the length (if so, then the length of the passage, and thus the size of the pyramid, was not arbitrary or altered, but planned from the start). But the height of ground level above the ceiling at the end of the passage of just over 55 cubits, and the height of the entrance above ground level of just over 34 cubits, when 34 and 55 are the first numbers in the fibonacci series giving a really accurate expression of phi, can not be explained away as an artifact of any other intention that I know of in the height of ground level above the ceiling of the end of the passage and the height of the entrance above ground level.

I believe that the presence of all of these phi proportions are cumulative evidence of the intetional use of phi in the dimensions of the pyramids.



Edited 1 time(s). Last edit at 08/23/2007 11:26AM by Jim Alison.