Summing up

1. The real great scandal about the pyramids of Gizah is that they have not been surveyed for almost a century. The survey that Petrie conducted in 1880 is of limited accuracy; he had the means available then to a private citizen operating on his own. Those who claim that the pyramids of Gizah were built without any mathematical accuracy could prove their point most easily by a survey. Such a survey has been conducted with a subsidy by the National Science Foundation for the three pyramids of Teotihuacan in Mexico. Why have traditional Egyptologists steadily opposed a survey of the pyramids of Gizah? Such a survey would be an easy task with the help of aerial photography. The truth of the matter is that Borchardt asked Cole, a professional surveyor, working for the geodetic survey of Egypt, to test the length and the orientation of the base of the Great Pyramid in order to bury forever, as he states, all the mathematical theories. I have shown that the Cole survey agrees to the millimeter with what one could expect from the mathematical point of view. This explains why the scientific surveying of the Gizah complex stopped at that point. We miss accurate data about the size of the two other pyramids, their orientation and about the mutual distance of the pyramids and all other buildings of the Gizah complex. Do Egyptologists deny that this is a true account of the situation?

2. An Egyptologist should answer this question: is it true that the Cole survey supports the proposition that the sides of the Great Pyramid have an average length of 439 ½ cubits? (4 x 439 ½ altogether). I do not have to ask anything more. Those of my readers who understand mathematics have seen that the rest follows logically. The total length of the four sides is 1/2 minute of degree of latitude at the Equator. Given a side of 439 ½ cubits, if the Pyramid has a slope 51° 51’ 14”, in agreement with the exact value of _ (the height of the pyramid relates to the perimeter of the base as the radius relates to the circumference) the height is 279.794 (almost 280 cubits). But the Earth is not a sphere, it is flattened at the poles. Hence, the slope was calculated by the Golden Section as 51° 49’ 38”, which makes the height 279.526. The difference between the two heights indicates the exact polar flattening of the Earth. This is the essence of my interpretation of the Great Pyramid. There are further refinements due to the slight differences in the length of the four sides.

3. I have given the figures for the length of the Egyptian royal cubit up to 1/10,000 of millimeter. I have related these figures to the units of weight and volume. If I am wrong, it should be very easy to disprove me. The remains from the First and Second Dynasty, which often fit the units I call Roman, have to be excluded. Other exceptions are in the late period, after the Assyrian conquest, when new units are imported from Mesopotamia. But these exceptions have nothing to do with the pyramids.

In my Harvard doctoral dissertation, submitted to Sterling Dow, then President of the Archeological Institute of America, in dealing with Greek coinage, I set my first reckoning. For technical economic reasons, documented by Greek inscriptions, the standard of the Athenian mint had to be 20/21 of the present English pound, that is, had to be 432 grams or 48 Egyptian qedet. According to my interpretation of statistical data on Athenian coins the scales of the Athenian mint were calibrated to register 1/6 of an English grain. Earlier when I was an Instructor at the University of Rome in the field of Roman studies, I had arrived at the conclusion that the Roman libra is 324 grams (5000 English grains); which means 36 Egyptian qedet. The weight of the libra determines the length of the Roman foot. All this can be verified. Starting from the above figures I tested the Egyptian evidence. If my figures for the base of the Great Pyramid are wrong it would take only a little effort to undermine the entire structure. I have related the Egyptian system of measures and the dimensions of the Great Pyramid to the size of the Earth according to the highest precision achieved by modern science. Even the figures published in the last three or four years support me (see p. 332, bottom of Secrets of the Great Pyramid).

4. Borchardt, who was the most militant opponent of mathematical interpretations of the Great Pyramid, wrote an article (Janus, Festschrift für C. F. Lehmann-Haupt) in which he dealt with measuring rods on which there is a standard inscription which states that the length of Egypt is 106 atur, divided into 20 atur for Northern Egypt and 86 atur for Southern, Egypt. These figures are repeatedly mentioned in Egyptian texts. If my interpretation of these figures is wrong, what is the right interpretation?

The table I submit on pages 329-330 [of Secrets of the Great Pyramid] was obtained by putting together all records I could find about local distances in Egypt. I would be glad to hear if there are records that I missed and that contradict me.

5. Three Pyramids. I am now trying to place an article that explains the mathematical relation between the pyramids of Gizah. There is a simple mathematical reason why the pyramids had to be three. The father of Cheops, Sneferu, was the first to build a true pyramid, and be built three pyramids. How do others explain the fact that Sneferu built three pyramids? How do these pyramids relate to each other? Why is one of the pyramids of Sneferu the peculiar Bent Pyramid?

6. Capitals of Egypt. In its dynastic period Egypt had three capitals.

A. Old Kingdom. Memphis is at latitude 29° 51’ N. The point Sokar in the necropolis of Memphis (present village of Saqqara) is at 29° 51’ N. 31° 14’ E. This is on the meridian of the middle axis of Egypt. The meridian cuts the Nile at the Second Cataract exactly 8° south of Memphis. Emory, the authority on the remains of the first three dynasties, announced as a great surprise the discovery of early dynastic monuments at the Second cataract, (New York, Times ). It was not believed that the Egyptians had extended that far.

Greek and Roman writers state that at Elephantine (24° 06’ N.) there is a place where the sun does not cast shadow at noon at the Summer Solstice. Is it not a scientific fact that in order for this to take place the Tropic must be at latitude 29° 51’ N?

Memphis was 6° north of the Tropic. The Great Pyramid is 6° north of 24 00 N, the upper limit of the First Cataract. Elephantine, the lower limit of the First Cataract is 6° south of the Apex of the Delta.

Is there any incorrect statement in what I say on page 296 [of Secrets of the Great Pyramid] about the hieroglyphic symbol for Southern Egypt?

B. Middle Kingdom. The capital moves to Thebes. Is it true or not that the central room of the Temple of Ammon at Thebes is at a distance of 2/7 from the Equator to the Pole?

Starting from the well-known point Pelusium, steadily mentioned in the texts as the eastern boundary of Egypt along the shore (31° 06’ N. 32° 36’ E.), follow meridian 32° 36’ E. inland from the sea. This meridian passes in front of the Temple of Ammon at Thebes in the middle of the Nile. Then this meridian cuts again the Nile exactly at latitude 23° 00’ N. at the point called Sacred Sycamore (near Tachompso). Along this meridian the distance of Thebes from the sea is twice the distance between Thebes and latitude 23° 00’ N. According to Herodotus there are 6000 stadia from the sea, at Pelusium, to Thebes and 3000 stadia from Thebes to the Sacred Sycamore.

These stadia make 1000 stadia to a degree of longitude at the latitude of Thebes.

C. Akhetaton. Tell el Amarna. There is general agreement that the new capital established by this Pharaoh was in a strange place. It was at 27° 45’ N., at the middle point of the distance of 7° 30’ (1/12 of the distance between the Equator and the Pole) from latitude 24° 00’ N. to Behdet (31° 30’ N.), the extreme northern limit of Egypt.

The position of the new capital is indicated by the so-called Boundary Inscriptions of this several copies were found all around the city. What is the meaning of these inscriptions, if it is not what I state on page 342? What is the meaning of the precise statement of Aknaton 6 atur, 3/4 khe, 4 cubits?

7. Greek and Roman Authors. All the modern speculations about the significance of the Great Pyramid have started from the statement of Herodotus (II. 124) that the surface of the faces is equal to the square of the height, which implies the Golden Section and a slope 51° 49’ 38”.

Was Herodotus an ”idiot” as Burchardt declares?

In my opinion Herodotus had perfect mathematical information about Egypt. All his figures about the dimensions of Egypt, given at the beginning of Book II of his Histories, are accurate to the minute of degree by a stadium of 1111.1 to a degree of longitude. Stadium of 225 Roman cubits of 99.8816 meters. It is a degree of 110,980 meters, correct at the latitude of Samos (latitude of Mycenae according to my terminology) which Herodotus mentions (II. 168). I am ready to hear a different explanation of his figures about the distances within Egypt. In spite of all the developments of modern Egyptology, Herodotus remains our paramount source of information about ancient Egypt.

As I explain at the bottom of page 371, I have examined all Greek and Roman writers other than Herodotus who deal with the Great Pyramid. I established that they all drew on a single writer, Agatharcides. They agree that the side is 1 ¼ stadium and that the apothem (slant height) is a stadium up to the pyramidion. In Greek usage stadium means 1/10 of minute of degree. Is there a different explanation for these texts?

8. Book of the Dead (see page 369, Secrets of the Great Pyramid). The most important chapter of the Book of the Dead states that the spirits of the Nether World are 4,601,000 and are 12 cubits high. These are most specific figures. Is there another explanation for these figures?

These figures were so important to the Egyptians that they are also referred to by Herodotus. This point got lost in the editing of the Secrets, but some of my readers who are mathematically minded got it from what I had said. The figures are in perfect agreement with what has been established very recently, with the use of satellites—namely, that the North Pole is 50 meters higher than the average based on the entire Earth. The Egyptian figures were intended to apply to the northern hemisphere.

How I Differ From Previous Interpreters.

A basic novelty introduced by me in relation to previous interpretations is the calculation by the pyramidion. I got it from. Agatharsides. Thanks to my basic training, which is in Greek and Latin philology, I was able to reconstruct from those who quoted it the original text of Agatharsides. The slant height up to the pyramidion is a stadium (1/10 of minute of degree) of latitude at the Equator. The slant height to the apex gives the stadium at the latitude of the Pole. Probably the pyramidion was graduated in order to give the value for all degrees between the Equator and the Pole. This is related to my basic discovery: all my predecessors tried to explain the Great Pyramid as if the Earth were a sphere. I was the first to recognize that the Egyptians took into account the fact that the Earth is flattened at the poles. This is the reason why the figures of my interpretation can fit the reported dimensions to the millimeter: I got the figure for the flattening at the pole from hieroglyphic text and from cuneiform mathematical texts. The pyramid confirms this figure, which is as good as contemporary science can achieve.