Our Cosmic Ancestors (10 page)

cubits and the apothem to 355.245. The volume now is exactly 18 million cubic cubits, but conditions one and two are not satisfied. As one can see from these examples, the three conditions are incompatible with modern mathematics using the decimal system. But the Egyptians did not use such a system; instead of decimal parts they used fractions. And if we use fractions, the problem can be solved.

For the Egyptians, as for all ancient mathematicians, the factor P1 was 22 divided by 7, or the fraction 22/7 with a decimal value of 3.142857. The factor PHI was the fraction 196/121, or 1.619834. If expressed as simple fractions, both factors are related because the square root of factor PHI is now equal to 4 divided by PI, 14/11, or 1.272727. Here you have the secret of the Great Pyramid, or at least one of them.

With this factor, 1.272727, and a half-base of 220, the height is exactly 280 cubits and the apothem 356.089. The volume is 18,069,333 cubic cubits. The first two conditions are fulfilled in Egyptian fractions but the third is not. To satisfy it, we will have to discover another secret of the Great Pyramid - that its base, contrary to previous assumptions, is not exactly a square.

One of the strange qualities of the Great Pyramid is the fact that its faces are not entirely flat. They are concave and the apothem recedes by about one cubit. The first to discover this concavity was Edme Francois Jomard, one of the French scientists accompanying Napoleon on his Egyptian expedition in 1798. A sketch of the Great Pyramid done by Napoleon himself is still extant and it clearly shows the receding apothem on the two visible faces.

This anomaly was forgotten for nearly a century until, in 1881, Sir Flinders Petrie rediscovered it and measured it to be 37 inches, or 1.8 cubits, on the north face. This value was too high, but what can you expect from ancient measurements? Besides, there is now an excellent aerial photograph showing the dihedral angle of the sides in superb clarity

As could be expected, each pyramidologist has his own explanation for this angle. The fact is that it renders the outlines more distinct and the shadows more recognizable. This was of great importance for the astronomers because it made their observations much more precise. Also the luminosity of the faces is enhanced greatly by the
two semi-faces forming the dihedral, and thus observations of the Sun, Moon, and stars by the line of the apothem are made much easier. This especially applies to observations of the stars Sirius, which was the base for the Sothic year, and Alpha Draconis, the star that was the north polar star in those days. The slight dihedral of the faces also reduced the volume of the pyramid to make it exactly 18 million cubic cubits, which for some unknown, but probably religious or astronomical reason, was of utmost importance to ancient Egyptians.

It is not possible now to measure the exact recession of the apothem because all of the exterior stone plates have been carried away, but the dimension can be calculated with great precision. With a base of 440 cubits and a height of 280 cubits, the surface of the base has to be reduced by 743 square cubits to obtain a volume of 18 million cubic cubits. That results in shortening the apothem by 0.521 cubits and receding its base by 0.844 cubits.

The most astonishing result of this arrangement is that it pushes back the two half bases of the pyramid by a quarter degree so that the two halves form an angle of 1/2 degree. This results in a difference of 2 minutes of solar clock time and could have served the ancient astronomers to set their water clocks or hourglasses to the exact solar time.

Let us have a look now at the angle of inclination of the faces. With the dimensions of 220 cubits and 280 cubits, the angle is 51
^°
, 50' 34", or 52 degrees in round numbers, which leads to another interesting discovery. We know now that in the distant past the poles of our planet have wandered considerably. According to the latest geological data, the poles seem to stand still for a period of about 30,000 years, then move around for 6,000 years and lie still in the new place for another 30,000 years. These cycles are in harmony with the solar constant and the ice ages.

It is now estimated that the present positions of our poles were established about 12,000 years ago and that they will stay put for another 18,000 years. Let's also remember that the inclination of the Earth's axis varies in cycles of about 42,000 years. With that in mind, we can return to the Great Pyramid of Cheops.
We can assume for a moment that the Great Pyramid was constructed at a time when the inclination of the terrestrial axis was 22 1/2 and the site of construction was at 29 1/2
⁰
N - explaining why the faces of the pyramid had an inclination angle of 52 degrees. Under these conditions the south face of the pyramid would at the time of the winter solstice be perpendicular to the direction of the Sun, while at the summer solstice the angle would be 45 degrees.

Now, it could very well be that the angle of 52
⁰
belonged to a smaller and much more ancient pyramid that now is inside the larger Great Pyramid of Cheops, a possibility indicating that the Great Pyramid might be much older than we believe and that Cheops was not the builder but only the enlarger of a smaller pyramid that could be anywhere between 5,000 and 20,000 years old. Nothing has been found so far that would allow us to determine its true age. And that might be one of the reasons why so many people, including Napoleon, were so utterly fascinated by this big heap of stones.

But why was the exact volume of 18 million cubic cubits so important to the Egyptians that the writers of antiquity never forgot to mention it? I might have found an answer to this question, too, even though this may lead some to think I'm so obsessed with the constant of Nineveh that I seem to find it everywhere.

We know that the pyramid was built in successive steps separated by long periods of inactivity. This was done for good reasons. First, the enormous weight of the construction needed time to settle and take its final position before the last corrections or realignments could be made. Then the observation platform at the top was probably used as an observatory during these building intervals to make adjustments so that the inner corridors of the pyramid would be precisely in line with the stars at certain times, especially with Sirius and Alpha Draconis which were the most important for the Egyptian astronomers. It has been found that 3,400 years before Christ, the ascending gallery was aligned with Alpha Centauri and the descending one aimed at Alpha Draconis, the polar star of that time. But the possibility exists that both these galleries could have been used similarly to sight two other stars separated by the same celestial angle several thousand years before.

Sir Gaston Maspero, director of the French archaeological mission in Egypt in the 1880's, found a curious hieroglyph in inscriptions around Sakkara. It showed a truncated pyramid with an obelisk on top of it supporting the solar disk. At first Maspero had no explanation for it. Later on, the conclusion was made that it showed the unfinished Great Pyramid of Cheops at the level where the ascending gallery terminates. The Maspero hieroglyph is an indication that the work on the pyramid was interrupted for a long time at its half height.

When the Great Pyramid was at the halfway mark, the surface of the platform was one quarter of the surface of its base and the volume of the pyramid to be finished was one eight of the whole volume. The finished part, therefore, was seven eights of 18 million cubic cubits, or 15.75 million cubic cubits. When you translate this latter volume into our metric system, it equals 2,268 million cubic decimetres and 2,268 million is the exact value of the Nineveh constant. We must add here that the ancient Egyptians were quite familiar with the metric system. In the same region of Sakkara, where the hieroglyph of the truncated pyramid was found, archaeologists have gathered metric standards used by ancient Egyptians.

Once more we find the great constant but expressed in cubic decimetres. Coincidence? A coincidence is possible, of course, but I have seen so many of these coincidences that I do not believe in `coincidences' any more. And then there was the discovery that the length of the granite coffer, which is not a coffin but a standard of measure placed in the king's chamber inside the Great Pyramid, is exactly 2,268 millimetres and that the total volume of the pyramid in cubic cubits multiplied by the historically sacred number 126, again gives us the number of the great constant: 2,268 million.

It seems that for the Egyptians, too, this number had a sacred meaning, which could mean that in different forms the Nineveh constant was known to the entire ancient world and that it was used for thousands of years until our Sacred Mother the Church systematically destroyed all traces of earlier civilizations. Moreover, this magic number has also been discovered at Teotihuacan in Mexico.

The majority of the scientists and pyramidologists who explored the Cheops pyramid tried to discover in its dimensions all kinds of mathematical and astronomical data. Some among them even invented new units of measure to adjust their measurements to the values they wanted to obtain. It is true that many astronomical data are to be found in the dimensions of the pyramid, but the most surprising aspect is that nobody thought of a much simpler solution that seems obvious to me. Could it really be sheer coincidence that each of the eight principal dimensions of the pyramid are exact multiples of planetary conjunction and revolution periods if we measure them with the Cheops finger of 18.719 mm, or 1/28 of the Cheops cubit?

These eight dimensions are the perimeter of the base, the sum of the two diagonals of the base, the side of the base, the edge, the apothem, the height, and the two perpendiculars drawn from the centre of the base to the edge and to the apothem. When measured in Cheops fingers, these dimensions give us the following numbers: 49,280; 34,850; 12,320; 11,720; 9,970; 7,840; 5,840; 4,840. As anyone can verify, each of these numbers is an exact multiple of some planetary revolution or conjunction period measured in days. For example, 4,840 is equal to 55 sidereal periods or 42 synodic periods of Mercury while 5,840 represents 10 synodic periods of Venus. This can be no coincidence, no more and no less than all the other inexplicable cases where we always find the same numbers and calculation methods.

Much has been written also about the purpose for which the Great Pyramid was built. My opinion is that the basic reason for it was to serve as an astronomical observatory. Because of its enormous dimensions, the shadow of the pyramid moved very rapidly on the ground and made it possible to measure time with great accuracy. Even the year of the star Sirius was measured that way and the Egyptians figured it at 365.250681 solar days. This value was abbreviated to 365 1/4 days that coincided with the civil year of 365 days every 1,460 years.

The Great Pyramid of Cheops was also a space beacon. Today millions of people around the world have become familiar with UFOs and the idea that space vehicles have visited our planet for aeons and continue to do so, so that the possibility of space visitors does not seem so strange any more. From high above, the pyramid is visible at a very great distance to the naked eye, and in space it shows on the radar screen much farther out because of its slanted sides that reflect radar beams perpendicularly if the approach angle is 38
^°
above horizon.
It is easy to calculate that the polished stone surface of nearly 21,600 sq. m on each face, is a radar reflector with a directivity factor of over 600 million for a 2 cm wave length, for example. Such a powerful reflector could have served as a beacon for the approach of a space ship and possibly has been serving for this purpose for a long time. We know that the pyramid had been painted in various colours, which could have been metallized to increase the reflectivity to laser or radar beams.

We have not yet talked about the next largest pyramid at Giza, the Pyramid of Kephren which is a true wonder of geometry and mathematics. It is built in proportions of 3:4:5 in strict adherence to the sacred triangle and the theorem of Pythagoras. The cubit which was used to lay out this pyramid's dimensions is seven-sixths of the ordinary cubit because by that time Lower Egypt had been annexed to Upper Egypt and the length of the kingdom had grown to seven-sixths of its previous size.

In reality, the architects who built the Pyramid of Kephren used another simple standard - five-thirds of the royal Egyptian cubit, that is, seven-eights of a modern metre, and this is one of the most direct correlations that I have found between the ancient measurements and the metric system. (Such is also the ancient Mycenaean 18-foot standard, that equals exactly 5 m.). To keep these measures separated, let's call the Kephren unit the `Kephren yard' as opposed to the 'Cheops cubit' that was the basic measure for the Great Pyramid.

The perimeter of the base for the Kephren Pypramid is then 984 yards, or 861 m; half side of the base itself 123 yards, or 107.625 m; the pyramid height 164 yards, or 143.5 m; and the apothem 205 yards, or 179,375 m. Each of the last three dimensions can be divided by 41 to give us proportions of 3:4:5. The base area and the volume of the Kephren Pyramid are both 87 per cent of those of the Cheops Pyramid, so that pyramid is not so small after all.

The smallest pyramid at Giza is the Pyramid of Mykerinos, the son of Cheops who was the successor of his uncle Kephren. This pyramid is about 72 m high and has a base side length of 108 m. At first glance it seems that it was built with a 30 cm foot, but precise measurements show that the unit used was the foot of 0.301845 m - a unit of length that could be more than 10,000 years old and was