I have several Giza related theories which I will describe in this page. Whether or not the theories are correct, they may serve as inspiration for others to find even better explanations for some of the greatest mysteries of Giza. I simply called the page "Giza Solved" as a convenient title. Of course, there will never be a way to positively prove which design methods were actually employed by the pyramid builders, unless something is unearthed someday that actually depicts it.
It is currently my belief that the Great Pyramid and others were aligned to the equinoctial Sun. The slight westward deviation would then be due to the fact that the Sun doesn't rise exactly due East on the equinoxes but slightly North of East on one day and slightly South of East the next. If the Egyptians were to align to the equinoctial Sun on the same date every year the exact angle of alignment would vary slightly from one year to the next and it would rarely be exactly due East. It can be only a few arc minutes off from due East one year and 15 or more arc minutes off the next, so there is no way to deduce the actual date of construction of the pyramids from their azimuths because the variation is too unpredictable.
What makes me think the pyramids were aligned to the Sun rather than to certain stars? Well, the causeways from the Great and Second Pyramids are aligned to the sunrise 30 days before and 30 days after the equinoxes respectively. That is three Egyptian weeks of 10 days. My guess is that they would have held some kind of 30 day ceremony leading up to the equinox and possibly a similar one after. What other purpose could the causeway angles have? They don't correspond to the "cross quarter point" sunrises, as suggested by some. That would be more like six weeks each side of the equinoxes. So it appears that Giza is very much concerned with the equinoctial sunrise, which makes sense when you recall that Khufu proclaimed himself to actually be the Sun god Re himself and both Khafre and Menkaure have the name of Re in their names.
No stellar alignment theory can explain Khafre's Pyramid azimuth being further West than the Great Pyramid's. Only a solar alignment at the equinoxes can produce such seemingly random fluctuations. Sometimes the equinox sunrise is slightly South of due East instead of slightly West. In 2505 BC, for instance, on October 14th the Sun rose at almost 14 arc minutes South of due East. That's the same day that the Sun rose at slightly North of due East in years such as 2593 and 2597 BC, matching the Great Pyramid's azimuth.
My theory on the shape of the Great Pyramid is that it was designed and laid out in a unit called the "Nippur Cubit", rather than cubits. I previously thought the dimensions were in "double remens" because the sides are very close to 311 double remens, which would be part of the pi fraction 311/99. A nagging problem with this theory was that the diagonals of the Great Pyramid's base should have been 622 royal cubits but is in fact slightly less than that. The only theory which explains the diagonals satisfactorily is one involving the Nippur Cubit.
Being that the Great Pyramid's height is 280 royal cubits, it would convert to (100 x sqrt 2) x 2 Nippur Cubits (NC for short), which is 282.8427125. That length is easily obtained as the diagonal of a 400 NC square. Multiplying that by pi yields 1777.153175 NC as the perimeter of a perfect squared circle type pyramid. Not knowing the exact value of pi, I believe that the Egyptians used a fractional version of pi, such as 311/99, to calculate the perimeter. That would yield 1777.052194 NC, which would have been rounded off to 1777 for simplicity. That would make each side of the pyramid 444.25 NC, producing a diagonal of 628.2643751 NC (2 pi) or about 621.9465 royal cubits. Using Flinders Petrie's survey coordinates for the Great Pyramid's corner positions we obtain diagonals of 621.966 RC from the NW to SE corners and 621.89 RC from NE to SW, the pyramid being slightly off square. As you can see, these are almost the exact theoretical length for my NC theory. The average of the two diagonals is 621.928, only about 2/100ths of a cubit difference from the theoretical 621.9465 cubits. about 0.4 inch. I'm using Petrie's royal cubit length for this, 20.62 inches.
So at the present time I can find no better explanation for the Great Pyramid's dimensions than that it is a representation of a discovery by the Egyptians or the Mesopotamians (who created the NC) that a circle with diameter the diagonal of a 400 NC square has a circumference of almost exactly 1777 NC. Why did they not simply use the same number of royal cubits instead of NC? Could have been some religious reason. Maybe that early discovery was seen as a sacred thing not to be altered in any way, such as using different units. All I know is that the diagonals of the pyramid's base confirm this NC hypothesis very nicely and that I can find no other explanation for the diagonals being slightly under 622 RC, which they would certainly have rounded off to if they were in fact using RC for the design. That would have made things much easier. They would have rounded off either the side dimensions or the diagonal dimensions for easy laying out. The sides have not been rounded off to 440 cubits, because they are actually around 439.8, so neither the sides nor the diagonals are in practical numbers of RC but the sides are in a practical number of NC because it is an even quarter unit, 444.25, which is easy to measure out.. The builders appear to have employed royal cubits in the interior structures but the outer shape is clearly in NC.
Royal Cubit Origin
As Theorized by others previously, my theory is that it was derived from the Nippur Cubit of 518.5 mm (20.41335853 inches) but through a different procedure. The procedure theorized by others is that the Egyptians divided the Nippur Cubit (hereafter "NC") into 28 "digits", originally being divided into 30 digits, and that 20 of those were used as the Egyptian "remen".
This method does work well enough and could be the true origin but I have found another possibility.
My alternative royal cubit theory is that the royal cubit (RC) was 1/311th of the circumference of a 100 NC diameter circle. I believe this was done because of the fractional approximation of pi 311/99. Having a unit of measure which is 1/311th of the diameter of a 100 NC circle would have been convenient because it makes for easy calculation of a circle's circumference. 311 combined with 99 is inconvenient because of 99 having very limited divisibility. 100 has much better divisibility. So with the new RC unit the Egyptians could more easily convert between a circle and a straight line by simply knowing its diameter in NC.
This is just an alternative possibility. The previously published method works out well enough but seems a little arbitrary, by which I mean it doesn't seem to have any particular purpose in mind. This circle based theory actually has a practical purpose behind it, which makes it more plausible in my opinion.
In regard to the possible use of sqrt 2 fractions in the Great Pyramid's design, there is another instance of the use of such a fraction, in the rectangle encompassing the three Giza pyramids. The width from the east side of the Great Pyramid and the West side of the third pyramid is the fraction 17/12 royal cubits x 1000. I actually used the middle of the West side for this rather than either West corner because the third pyramid is rotated clockwise by about 13 arc minutes which is quite significant. More precisely, I drew a circle inside the pyramid base and used the middle of its left side. 17/12 x 1000 is 1416.666. From the middle of the right side of the Great Pyramid's inscribed circle to the middle of the left side of the 3rd pyramid's inscribed circle is 1416.6425 royal cubits, using an AutoCAD drawing of the three pyramid bases drawn to Petrie's survey specifications. This is, therefore, the exact distance and it matches the 17/12 sqrt 2 fraction to within 2/100ths of a cubit, less than half an inch. Nobody else has ever explained why the width of the Giza rectangle is not the true value of sqrt 2 but somewhat over. It is simply because rather than construct an actual 1000 cubit square on the ground and use its diagonal they instead used the fractional approximation of sqrt 2. Why they did that and why they chose that particular sqrt 2 fraction is known only to the designer. What I can say with good confidence is that they apparently did.
Now what about the long side of the rectangle? Well, I got a length of 1733.4341 royal cubits, which appears to be based on the fraction 26/15 (1.7333).
This diagram shows my theory on the Grand Gallery angle, reported as between 26 17' and 26 18'. Squares of 16 cubit sides are drawn on both sides of the King's Chamber and a circle is drawn using the square's diagonal as its radius. It's intersection with the square on the right determines the angle of the Gallery. Incidentally, the Queen's Chamber appears to have been designed to be positioned so that the peak of its ceiling is exactly 37 double remens up from the base. 37 is the 12th prime number.
The two rectangular planes formed by these two procedures are identical in length except for a very slight excess of about 1/32 inch in the top view plane. The answer was to simply shorten that plane by that amount so that it could form a single rectangular block. That shortening resulted in the sqrt sqrt 15 rectangle on the end of the top being reduced to a mere 3 decimal places of accuracy. If we then add up the numbers that were used for the square roots on the sides and on the top we get 7+7+15=29 for the top and 20+17=37 for the sides. Now we make a fraction using these two numbers. Since there actually is no lid for the coffer, we have to put the 37 on the bottom of the fraction, the sides being above the bottom of the coffer (which obviously has the same dimensions as the top view). This gives us the fraction 37/29. This comes out a decimal number of 1.275862069, which is sqrt sqrt sqrt 7, accurate to three decimal place, the true figure being 1.275373107. So it's off by only about 5/1000ths.
In regard to the inner dimensions. The diagonal of the inside is simply 4 cubits and the depth is simply 1 1/3 cubit. They made the wall thicknesses such that a rectangle of those dimensions is the same distance from the outsides all around.
As shown below, the diagonal distances are simply 5 and 7 cubits. The diagonal across the end of the chamber is 15 cubits, which produces a 3,4,5 triangle across the full chamber, as published by others previously. An interesting thing here is that, as shown by the light blue rectangle, the height of the chamber is also the end dimension of a 1:2 rectangle with a diagonal of 25 and side lengths of sqrt 5 x 10. Another way to look at it is that the chamber height is 1/2 of sqrt 5 x 10. The light blue part of the diagram is not part of the actual chamber, it's just to show the relationships I mentioned.
The height of the side walls of the chamber are reported by Petrie as 184.47 inches, which converts to 8.946168768 cubits. The dimension which I believe it to have designed to be is shown on the extreme left in the diagram, as 8.9571068 cubits. That's within about 1/100th of a cubit from Petrie's data (less than 1/4 inch), sufficiently close by any reasonable standard. Some investigators have assumed that it was meant to be an even 9 cubits but the actual measurement is too far off from that figure to be plausible, considering how exact the 10 and 11 cubit dimensions are. The 11 dimension is actually 11.03297769 cubits (227.5 inches), from Petrie's measurement, and the 10 dimension is actually 9.983026188 cubits (205.85 inches). So you can see that it would be illogical that the height would be off by such a large margin in comparison.
As Petrie theorized, I also maintain that there was originally a layer of flooring stones in the chamber. I theorize that this layer was exactly 1 remen in thickness, a remen being the side length of a square with a diagonal of 1 cubit. Such squares are known to have been used by the ancient Egyptians and is known as a "construction remen". So it is certainly reasonable for the flooring to have been such a thickness. The fact that it works perfectly is a very strong indication that this was, in fact, the actual thickness employed.
The height of the peak of the ceiling is found to be the same as the height of the King's Chamber, which is not an even cubit number. Petrie's measurement for the peak is 245.1 inches, which is 11.88651794. When we add the floor thickness to the height shown in the diagram we get 11.88744667 for the full height of the chamber from base to peak, virtually the exact same number.
The obvious reason for the seemingly odd height of the walls above the flooring, 8.25 cubits, is found to be due to the objective of forming a 3,4,5 triangle as shown, while having the ceiling stones at an angle close to 30 degrees, the angle in the diagram being 30.4147244. They would have found that making the height 8.25 cubits and the length 11 cubits accomplished that goal while using easily measured lengths.
My theory is that it is positioned southward from the Great Pyramid a distance from its NE corner of sqrt sqrt sqrt sqrt 2 x 1000 (1044.273782) Royal Cubits and that the spot between its paws right in front of its chest (where the stelle is located) is sqrt sqrt sqrt sqrt 7 from the same pyramid corner. This is shown in the image below in red.
Obtaining the 4th square root of a number is an easy matter through simple geometry. The fact that both distances are 4th square roots would be very unlikely were it not purposely designed that way.
In the image, you may notice that the third pyramid doesn't seem to match up exactly with the CAD image. I don't know why that is. I used Flinders Petrie's survey triangulation data to position all of the pyramid corners. This is an exact replica of Giza from Petrie's coordinates. Maybe his survey was inaccurate in the case of the third pyramid or maybe that part of the Google Earth image is a little distorted, I don't know. The other two pyramids match up nicely though.
I also have a theory about the Giza pyramid layout on this page
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