Were the three famous Giza pyramids laid out as a group, or independently of each other? The best way to tell is to investigate geometric and numeric relationships in the pyramids' layout. Subsequently to the provision of reliable measurements from the geodesic survey of Giza by Sir William Flinders Petrie, a century-worth of testing has revealed great many relationships. No one has been able to derive the layout with complete accuracy, however, and so builders' mistakes are called upon to explain the discrepancies between Petrie's plan, and the proposed reconstruction. We have competing theories, which sometimes contradict each other. Uncertainty then adds weight to the perennial objection from critics in like cases:

"You can use mathematics to derive the position of anything... such as the cars parked on my street."

Skeptics stick to the opinion that even the most ingenious design means absolutely nothing without discovery of the original plans, or a signed statement from Imhotep himself. There is a kernel of truth in all these objections. There must indeed be a number of ways to recreate Petrie's Giza layout of the three pyramids. But one should be forewarned that if the layout is random to begin with, even the most efficient procedure will likely be quite complex, and the more so, the closer to the original the recreation is to be. It is difficult to describe a chaotic position by a brief and highly abstract procedure (algorithm). I believe that these principles will apply in general to any three oriented squares like the pyramid bases tossed randomly upon a 2-D plane. By the same token, it would follow that if there were discovered an elegant and easy method of developing the Giza layout exactly, it should be enough to prove, or at least make highly likely that it is the essence of the original plan.
What about the skeptical claim that a bit of fiddling around would net a competitive solution of its own? A century of limited success in this very department by a number of researchers exposes it as just boasting.
John Legon and Robin Cook abstract a cohesive system from the Giza position, whereby they start out from scratch, with just a simple idea, and develop it step by step into a plan closely resembling the Giza layout, or more accurately put, Petrie's plan. This introduces the possibility that their recreations mirror what the Egyptian planners had done, before the builders strayed from the plan, just as expected for the historical period, and such a titanic task. In these cases, the picture we get is that of a brilliant, but early civilisation, adequately low in technology, and nothing to worry mainstream Egyptology or History.

I have found inspiration in Legon's and Cook's work, and was able to coordinate some of its elements against the background of my own ideas, resulting in a unique procedure for the recreation of Giza's layout. The problem is at once the reconstruction's greatest strength - it is exact. That was not supposed to happen by the present paradigm. Of the twelve pyramid sides, ten are exactly on the line given by Petrie, because all discrepancies fall completely under the radar scanning for errors.
While the recreated south-east corner of the third pyramid works out to being less than 1/10 millimeter from the position given by Petrie, the south-west corner strays 1.2 inches to the west. Since the reconstruction of the third pyramid depends on these two corners, two of the sides then end up being 1.2 inches longer.
Yet, with the exception of the north-east corner of the Great Pyramid, the positions of all the other corners depend on this south-west corner of the third pyramid being right where it is. It is absolutely pivotal to the success of the rest. In my opinion, it is fully justified by this success. Moreover, this corner by being in its place, creates another record of Pi to be found in the Giza pyramids, this time a record of the approximation of Pi, as the ratio 355/113. Apparently, Petrie had some difficulties measuring the third pyramid because of ruination, and that could explain the discrepancy.
Although this recreation serves to confirm the great value of Legon's and Cook's ideas, above all, it says a lot about the Egyptian planners, and builders. Accepting my solution as essentially selfsame with the original plan would do more than just raise high the bar of Egyptian knowledge of mathematics. The dynamic nature of the plan's development all but eliminates the possibility that it could have been drafted. Considering the scale of Giza, and the finesse of the method, the work to be done is virtually subliminal, small enough to be invisible on the biggest drawing board. So, the other possibility must be that the Egyptians had worked the plan out by calculation. Thus, their knowledege of mathematics had to be on a level categorically unreachable for a civilisation just several centuries past the hunter-gatherer stage.
In this case, speculation about advanced prehistoric science, which had somehow continued to exist in dynastic Egypt in secrecy, simply cannot be avoided. That is unless this solution is taken to represent 'just another one of those series of consistent coincidences' so typical for the Great Pyramid, and Giza. Meanwhile this reconstruction satisfies all criteria, which differentiate it from random. The sandheap for the proverbial ostriches just keeps on getting smaller.
Regardless of complications in evaluating the meaning of this discovery, it is now a matter of public record that Petrie's layout of the three pyramids can be produced by an exact method, easily, quickly, and with maximum accuracy.

There was an interesting change in my sentiments, as the study had progressed. Now, I don't marvel anymore at how close the reconstruction is to Petrie's plan, but rather at how close Petrie's plan comes to this set of exact ideas. I will carry it with me for the rest of my life, since it is not only unforgettable, but also easy to remember. Almost all of the reconstruction is pure geometry, which begins with a golden rectangle, and proceeds to duplicate Petrie's plan for the Great and Khafre's pyramids without a fault. Only then it is really necessary to recall two numbers in order to be able to perfectly pinpoint the third pyramid's south-east corner. One number, 113, is sometimes called magic, and the other number is the square root of 3, given to five decimals. The latter number is needed to set the scale for the design.


Establishment of the length of the Royal Cubit
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Read the rest of my report: [www.vejprty.com]