Hi Robin,

I have given your ideas some thought.

In 2006 I explained the design of Khafre's pyramid as having an intended side-length of 411 royal royal cubits and a projected height of 274 royal cubits from the seked of 5 1/4 palms, as detailed on page 29 of my monograph on the Grand Gallery of the Great Pyramid.

I had thought that this was obviously the case, but I see that you propose 411.16 royal cubits to fit a complex overall geometric plan of the entire site. This side-length converts to 411 royal cubits 4.48 digits, which hardly seems likely, unless you can identify a symbolic reason for this length.

Khafre set about building the most spectacular pyramid that the world had ever seen, just as Khufu, Sneferu and others had done before him. The challenge facing Khafre's architect was to build larger or steeper than Khufu's pyramid.

Ingeniously, the architect chose a site right next to Khufu's Great Pyramid, and drew up plans such that the peak of Khafre's pyramid would clearly rise above Khufu's pyramid. The evolution of pyramid building indicates that the quest was to build larger and steeper. In this case Khafre also chose a slope steeper than Khufu's pyramid.

Just recently a friend of mine visited the pyramids of Giza, and thought that the middle pyramid (Khafre's pyramid) was 'the Great Pyramid'. I had to explain that it was called the Great Pyramid in antiquity, but that all the fuss about 'the Great Pyramid' now refers to Khufu's large truncated pyramid at the end.

Your proposition is that Khafre's pyramid was the masterpiece of the three pyramids of Giza. The position of Khafre's pyramid could have been worked out by Khafre's architect, and was not necessarily contemplated during the build of Khufu's pyramid, so I see no reason to disagree with the idea without considering it further.

Your plans show merely show the bases of the pyramids. Byrd has pointed out there may be much more that has to be taken into account, but it may be that there is one layer of symbolism in the position of the pyramids which can be observed independently from the temples, walls etc.

The peak of Khafre's pyramid was certainly intended to be higher than the peak of Khufu's pyramid, and to the modern mind this inevitably means higher above sea level, like points on a map corresponding to triangulation stations on the top of hills and mountains. I have been criticised on this forum for using the word 'latitude' to argue for a geographical location based on the elevation of the pole star. Similarly, the connection to sea level was not necessarily obvious to the ancient mind.

The pyramid builders probably achieved level bases by cutting channels for water, and would have observed water flowing down the Nile, so it may have occurred to the architect that there was an absolute base level at sea level, but the determination of that level, had it been attempted, would probably have had a significant error, so that hypothetical ancient schemes based on a modern survey levels are most unlikely to be correct. Ignoring this fact is like burying your head in the sand of the sea shore when you certainly know its at sea level, and when others tell you that the tide is coming in. You know sea level relative to the peaks of the major pyramids, but to suggest that the Egyptians determined precisely the same levels is, in my opinion, very unlikely indeed. The tide of opinion is against you on the notion of sea level, so it is hard to regard your theories as anything other than dead in the water, which might not be the case without the sea level label.



Do Dr Lightbody's ideas on the layout of pyramid enclosures invite us to consider an area within an area?

If so, then this fits in well with my idea of squaring the circle, then building the pyramid within the area of a virtual square. For Khufu's pyramid I have proposed that there was a virtual square, just beyond the true base square, with a side length of 365 times the displacement of the Niche (in the Queen's Chamber), and that the east side of the foundations was built first at precisely this length. On this basis the perimeter of the virtual square was 1,460 times the displacement of the Niche.

I now propose that the design of Khafre's was also based on the number 1460, representing a perceived cycle of 1460 solar years in 1461 calendar years of 365 days.

If we take a circle with a circumference of 1,460 royal cubits as symbolic of the cycle of 1,460 solar years, and square that circle, then we get a square with a side-length of 411.77.. royal cubits, which is very close to 411 3/4 royal cubits, as calculated from the pi approximation 22/7 latent in the dimensions of the Great Pyramid.

For the 'area within an area theory' or rather 'square within a square theory' to hold good then the base side-length must be less than 411 3/4 royal cubits.

I note that this does not rule out your 411.16 royal cubits for the base side-length of Khafre's pyramid, but I am attracted by a base side-length of 411 royal cubits for at least five reasons.

1. I prefer the idea that the builders were instructed to build in a round number of royal cubits, in the absence of an irregular length with symbolic merit.
(It would not have built at 411.16 to fit an overall plan, when it could have been re-positioned to take into the 0.16)

2. 3/4 royal cubit is the horizontal distance in the 'run' of the 'rise and run' of the slope of Khafre's pyramid. The seked of 5 1/4 palms is a rise of 7 palms (1 royal cubit or 28 digits) for a run 5 1/4 palms (21 digits), and 21 digits is exactly 3/4 royal cubit:
The 'inner base square' is 3/4 royal cubit less in side-length than the 'outer virtual square'.

3. The propose virtual square, symbolic of the cycle of 1,460 solar years, is exactly 1/2 royal cubit below the pavement as a projection of the sloping faces, so the virtual height of the pyramid was 274 1/2 royal cubits; (1/2 royal cubit higher than the height of 274 royal cubits as the level of the peak above the pavement).

4. A base side-length of 411 royal cubits and the seked of 5 1/4 palms was the design that I proposed in 2006, with no theories other than the seked as the unit of slope, and an apparent length for the royal cubit of 20.62 inches, which is very close indeed to other determinations at Giza. (I have not invented this design to fit my new '1460' theory.)

5. The proposed seked of 5 1/4 palms is widely agreed by others, and the the proposed base side-length results in a vertical height with a round number of 274 royal cubits. I expect that many others proposed this design long before me. (The geometry still holds good even if the seked was not the unit of slope in the Pyramid Age).



Your illustrations are superb, but I can't agree with the sea level theory.

Mark