Great Pyramid Secrets Revealed
The Dimensions
The first Great Pyramid secret I would like to discuss is how the side lengths may have been laid out. The surveyed lengths of the sides of the base, according to Flinders Petrie, are an average of 9068.8 inches. Petrie's length for the Royal Cubit, deduced from all available sources, is 20.62 inches. That works out to 9068.8/20.62= 439.806 Royal Cubits for the side lengths. Obviously that is not the 440 commonly reported in most references, they simply assumed that 440 was the intended length and somehow all four sides came out short of it. I think I can explain the actual surveyed lengths, rather than assuming they were intended to be longer than they actually are, which obviously is not science but rather "making things up", in common parlance.
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I theorize that the ancient Egyptians, or at least the ones involved in the pyramid design and construction, used a version of pi which they obtained by taking the diagonal of a 1 Royal Cubit square and adding 30 Royal Cubits to it. I believe they noticed that the circumference of a circle with a diameter of 10 Royal Cubits was almost exactly the figure I just described, which is 31.414213562373. Since the true value of pi, approximately 3.14159265359, multiplied by 10 is remarkably similar to the square root of 2 plus 30, it seems unlikely that it would have gone unnoticed. Since it would be difficult to set out a length with the long decimal chain of true pi by mathematical calculation, it would have been very convenient to simply use the diagonal of a square with 30 added to it, because the diagonal of a square is already a long decimal chain so close to the required figure and no calculation is involved at all. The result is actually much closer than using a fractional approximation such as 22/7 and multiplying it by 10.
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How would the builders actually set out the lengths of the sides on the ground? They could simply use 14 of those lengths. 14 times 30 is 420, so they would measure 420 cubits and then add the diagonal of a 14 cubit square. The result would be 439.79898987 Royal Cubits (rounding to 8 places), incredibly close to Petrie's mean side length of 439.806. So this is a very a plausible explanation for the actual surveyed side lengths of the Great Pyramid of Giza, using a very simple and practical methodology based on an observation that the circumference of a 10 unit circle is almost exactly 30 units plus the diagonal of a 1 unit square. The height of the Great Pyramid is simply half the diameter of a circle of that size, which is 280 cubits, the pyramid being based on a circle of diameter 560 cubits. Why they chose that particular size for the circle is anyone's guess. I previously theorized that they used the pi fraction 311/99. That's possible but wouldn't help with the practicality of actually setting the side lengths out on the ground. That fraction yields lengths of 439.7979 repeating, which is virtually indistinguishable from the 439.79898987 produced by the method I described. By the way, true pi would produce sides of 439.82, so we know they didn't use true pi but something very close to it. Pretty much has to be either 311/99 or the method described above to account for the actual side lengths. Maybe they used both versions depending on the situation, the sqrt 2 version being the most practical for actually laying things out on the ground.
Chamber Positions
My current theory is that they were based on Procyon and Gomeisa when the latter was due West near the horizon, shortly before setting, around 3000 BC. Those are the two brightest stars in the constellation Canis Minor, which was seen by the Egyptians as Anubis, god of mummification among other things, obviously appropriate for a pyramid and a coffer chamber. Procyon would rise about an hour before Sirius. At dusk, Sirius would lead Procyon into the Underworld. The reason why the base of the pyramid image, or the ground (light blue pattern), is slightly above the horizon line in the star image, I assume, is because of the local terrain. The line in the astronomy simulation is an idealized perfectly flat horizon.
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It appears that there may be a chamber at the position of the star which is on the central axis below the Subterranean Chamber, which is called 13 Monocerotis. Presumably the tomb chamber would be underground on the central axis of the pyramid, where it would be surrounded by water like in the "Osiris Shaft" excavated recently by Zawi Hawass. Canis Major is on the left, with the bright star Sirius clearly visible. Orion is directly below the axis, which may also have played a role in the positioning. You can only see one of Orion's arms in this image but the whole constellation can be seen in the image below that one.
Lower view of the sky, showing position of Orion. Isis in the form of Canis Major is to the left, presumably crying over the fallen Osiris/Orion
The final image shows that when Procyon is in the eastern sky the constellation Leo appears to be gazing at it with its head above the horizon, much like the Sphinx has its head above the Sphinx enclosure and ground level. I don't know whether this was the basis for the Sphinx being that way or not, but it looks like a possibility.
