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IV. The Pyramid

If a society decides to harness the energy of the fabric of Space then the most obvious thing to do is to create a piece of Matter that can be used as a reference frame attached to a symmetric tensor. Because in an abstract geometrical reference frame there are eight octahedral planes, the most obvious piece of Matter is an octahedron or a body in close relation to this octahedron. Thus, this reference frame can be represented by a pyramid having equal edges which is a half octahedron. As this thing has been built in the remote past then, according to the present speculations, one can infer that it may have been done specifically for this very purpose. The problem is that the existing pyramids have dimensions different from a half octahedron. Take, for instance, the Great Pyramid of Giza. Its dimensions, as reported in many places in the WWW are: the base side, b = 230.36 meters, the height, h = 146.73 meters, the angle of inclination of faces to base α = 51.83333 degrees. The specific relations for an ideal half octahedron are

(25)

They are obviously not satisfied by the Great Pyramid measures. The difference is, however, small. Especially the difference in the angle of face inclination is only about 3 degrees while, at its current base side measure, the corresponding height must be some 163 meters in case it were an ideal half octahedron.

     As the idea that the pyramid is indeed an ideal reference frame seems most attractive in explaining the economical and human investment for building it, we may want to find an explanation of the difference between the real existing pyramids and the ideal half octahedron. There are two possible explanations. First of all our ancestors may have had information about some kind of anisotropy of Space, so that they have built the pyramid as it is today. This fact seems very unlikely, inasmuch as nothing can remain unchanged in the Universe. Another explanation can be offered by the very change of the Matter in Universe, particularly of the Earth itself. Let us explore a certain face of this idea.

     There is evidence that the Earth expands. Of course, there is also evidence of the contrary, but let us take this side of the coin, as it can explain the current difference of the Great Pyramid from an ideal half octahedron. One of the causes of this expansion may be the continuum creation of the matter, as advanced by some modern cosmological theories. The specific rate of the creation of the matter is very small to be noticed on a daily basis. One typical value (Gittus, 1975, 1976) would imply a growth of the Earth Radius with about 2 centimeters per century. This slow process would have influenced the Great Pyramid by enlarging its basis, which might have caused a sort of creep process with the result we witness today. Assume that the Great Pyramid has indeed been constructed as a perfect half octahedron, and describe its deformation as a creep process at constant volume. Within this assumption it is possible to determine the initial dimensions of the pyramid. Indeed, we have at our disposal two equations:

(26)

representing the constancy of the volume and the characteristic property of the ideal half octahedron. Here δb and δh represent the variations of the two dimensions so that (b – δb) is the initial base edge, while (h + δh) is the initial height of the pyramid. Solving the system (26) gives the initial values of base side and height

(27)

With the current values of h and b for the Great Pyramid of Giza, these variations amount to

(28)

In other words, the Great Pyramid was initially some 11 meters taller and some 8 meters narrower. At a rate of expansion of the Earth’s radius of 2 centimeters per century, the value δb places its construction some 7.884247/.02 = 394.2124 centuries ago. In other words it is by far much older than the currently accepted age, and has been built at a time when the Earth radius was some 1.5 meters shorter. This effect can hardly make an observable by itself, but can certainly make an observable in the pyramid.

     Along the same line of thought, the three pyramids of the Giza Plateau may not have the same age. Indeed, judging by the angle of faces, Menkaure should be just about the same age as Khufu (51.3 degrees) while Khafre is much younger (53.2 degrees). However, applying the very same calculations as before, we have indeed an age of 200.3452 centuries for Khafre, while Menkaure gives an age of 223.2073 centuries. This fact places indeed the Great Pyramid as the oldest among these constructions showing nevertheless, either that there may be some errors in estimating the current face angles, or that, in estimating the age we have to give up the idea of constant volume evolution, because there does not seem to be a straight correlation between angle and age. Such a correlation would place Menkaure’s angle around 53 degrees, according to its age, not 51.3 degrees as currently reported.

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