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Giza Solved
This is my theory on the positions and sizes of the three pyramids of Giza.
I theorize that the two major Giza pyramids were positioned to depict the two brightest stars in the sky, Sirius and Canopus, at a particular time in history, that being the early reign of Khufu. The third pyramid was simply a later unanticipated add-on and has no connection to the other two aside from mathematical, as I will now describe.
The height of the Second Pyramid was established by dividing the height of the Great Pyramid by the 5th successive square root of 2, this being 1.021891149, producing a height of 274.0001774 Royal Cubits based on a Great Pyramid height of 280 Royal Cubits. I know it may seem unlikely that the Ancient Egyptians would calculate successive square roots of square roots but we know that the Babylonians before them had the capability of calculating square roots quite accurately and it therefore is not implausible that the Egyptians would have possessed the same capability.
Once they had calculated the square roots of all practical sized whole numbers, the next logical step would have been to attempt to calculate the square roots of the square roots. Of course, since the square root of 2 is an irrational number, it's not possible to calculate its following square root with complete accuracy, but you could get reasonably close. Since 2 is the lowest number whose square root they would have worked with, it is certainly not unreasonable to accept the notion that they would have calculated its successive square roots to at least several levels. Certainly going as far as the 5th level is something that is quite plausible. Maybe that was as far as they went or maybe they had some particular reason to choose the 5th level for the height ratio of the two largest pyramids. I could only speculate on what that reason might have been, such as the 5 gods Osiris, Isis, Set, Nepthys ans Horus.
The simple fact that this procedure produces a perfect correlation with the actual heights of the two pyramids indicates to me that it must be taken as a real possible explanation. I believe that they started with the heights and then the widths of the bases were merely the result of applying whatever slope ratio they chose. This is supported by the fact that the base lengths of the Great Pyramid are not precise Cubit dimensions and the base lengths of the Second Pyramid are such an odd number as 411. It certainly does not appear that the pyramids were started with particular base dimensions but rather particular height dimensions.
I know that there are theories that the pyramid bases were sized based on certain square root ratios, this being the theory of John Legon. The fact is that this theory does not work out perfectly but is only a close approximation, although a very good one and one that could hardly have gone unnoticed by the designers. Maybe this property is simply the result of starting with the heights in a precise square root ratio, as I described, and then employing the particular slope angles used and maybe that was one reason why they used those particular slope angles. Maybe they found that designing two pyramids in that height ratio and then using slope angles based on pi for the larger one and 3,4,5 for the smaller one resulted in the bases having certain square root relationships on the ground when positioned to match Sirius and Canopus.
The height of the Third Pyramid was later established by simply dividing the height of the Great Pyramid by the square root of 5, a much simpler ratio. Using a Great Pyramid height of 280 Royal Cubits of 20.62 inches, this produces a height for the third pyramid of 2582.032415 inches. Petrie gives a height of 2580 ± 2 inches. Rather unlikely such a close match would be coincidental, considering what an odd number square root 5 is.
The side lengths of the third pyramid are simply the result of applying the chosen slope angle, which is about 51 degrees, to the chosen height, which was derived, as just explained, from the height of the Great Pyramid. The pyramid was positioned so that its South side was a distance of square root 3 x 1000 cubits from the North edge of the Great Pyramid and its West side was positioned so that it was 1/4 of the square root of 2 x 1000 cubits from the West side of the second pyramid. The first two pyramids were positioned to match the positions of Sirius and Canopus as I will now show.
Sirius was probably the single most important
star to the Ancient Egyptians, used to predict the inundation of the
Nile and to set calendars. It was also associated with the goddess
Isis. Khufu founded a temple of Isis next to the Sphinx, so we have
reason to believe that he had reverence for this goddess. Canopus is an
obvious choice for the star depicted by the second pyramid, being close
to Sirius and almost as bright. It was known as the Star of Osiris, so
with Sirius and Canopus we have representations of both Isis and
Osiris. Argo Navis was seen as the ark on which Isis and Osiris rode
during the flood.
Shown below is the view looking South in 2589 BC, the start of Khufu's reign, at a time of year when Sirius and Canopus would be visible. You can see the constellation Argo Navis fully visible on the horizon, similar to the boat found buried on the South side of the Great Pyramid. The exact time shown is when the star Alpha Pictoris is setting on the horizon.
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