Against an Egyptian Origin of the Giza Pyramids (cont.)
By Nick Kollerstrom, PhD
The eternal splendour of the two great pyramids at Giza involves some kind of relationship between them, and that connection is concretely expressed by two angle bisections. The First pyramid's descending passage angle is a simple 1:2 slope, a sekhed value of two, so its angle is 26° 33', which bisects the slope angle of the 2nd pyramid. That used the 3-4-5 Pythagoras triangle, the first in human history. We can write that exact relationship as
arctan (½) = ½ arctan (4/3)
That is pyramid maths! That bisection surely has to be intentional. It has to be intentional because it is symmetrical, each descending passage bisecting the other's outer slope angle. If you only had sekheds, how could you do this?
It is widely agreed that the Great Pyramid slope angle involved a use of the 22/7 pi-approximation. (4) But Egyptian maths did not 'square the circle' in this manner, by equating the circumference of a circle with the perimeter of a square - only the Greeks did that, aeons later. What it did (in the Rhind Papyrus, c.1700 BC) was, to find a circle having the same area as a given square, by using an 8:9 ratio. This was equivalent to having pi as 3.16, no doubt impressive for ancient times, and books compare that to the more exact 3.14 pi value expressed in the Great Pyramid's slope angle - however, these are very different kinds of problem; only from our modern viewpoint can we move easily between the two.
The square root of two links the Great Pyramid to John Legon's ground-plan design. (5) The distance from the top of the pyramid to the base of the King's Chamber, in relation to pyramid height, exactly expresses the root-two value. Egyptian units of measure contain this concept, insofar as they convert from area to linear measure, (from remens to Royal cubits) but as far as anyone knows they did not have a precise value as here used.
The height of the King's Chamber was exactly proportioned with the sole purpose (as far as anyone knows) of placing an integer 3-4-5 Pythagoras triangle in the diagonal plane of the chamber. This ingenious 3-D structure is way outside what we know about early Egyptian math. That's enough about math arguments, which are not everyone's cup of tea.
The Legon Ground-Plan
We focus here upon the Second Pyramid, as having been built upon quite sloping ground, 3-6° of incline. In one corner, a huge expanse of solid rock was 'bulldozed' away to make a level surface, while at the other end huge cubic blocks of three metres side-length, weighing some two hundred tons each, were used to build up the level surface. That trouble could have been avoided, by moving the site a short distance, indicating that there was something vital about that location. Quoting Robin Cook, who wrote two books about the Legon ground-plan: 'Why else build up the eastern side of Khafre's pyramid on a giant megalithic platform when, a short distance West, it could have been founded upon natural rock?' (6) Ralph Ellis has also commented upon how this second pyramid had been 'countersunk into the bedrock:' 'The Bronze Age solution to this defect on the topography of the chosen site was 'simple': just form a thick raft of megalithic blocks, each weighing in at hundreds of tonnes, and then build the pyramid on top of that.' (7) These vast blocks were finely-jointed to fit meticulously together. (8) Ellis like others discerned a stark contrast between this 'truly astounding' feat and construction of other, non-Giza pyramids: 'If one looks at the third and fifth dynasty pyramids, the engineering solutions are all simple and man-manageable.' Imaginative accounts of toiling Egyptian slaves have failed to take account of this primary phenomenon, which shifts the whole construction back into prehistory.