mercredi 22 février 2012
Do Satellite photos confirm theory of degrees?
Figure 1: Satellite photo of the Cheops pyramid (License GeoEye to H.D. Bui)
Figure 2: Inverse 3D Building
Figure 3: Observed bands and the Petrie sequence of stones (Drawings after J. Rousseau, Construire la Grande Pyramide, L'Harmattan, 2001)
Satellite photos are displayed in a 3D view when the Satellite is nearly, but not exactly, at the apex of the Pyramid. The faces of the pyramid are non-isosceles triangles, Figure 1. Even if the photo has a very high resolution, about 50 cm, it does not reveal anything particular, except the strata. For a comparison between the four faces, in order to have the same contrast and brightness, it is more convenient to have a 2D view of the Pyramid as a perfect square with its diagonals, or a 90° 3D view. We need the inverse of the so-called “3D building” of Google Earth. The ideal case occurs when both the Satellite and the Sun are at the apex. Google Earth technique is similar to the operation used in Chapter III of my book when I raised the 2D densitogram to obtain 3D views with hidden faces.
3D Building with a camera looking at all faces of the pyramid, as well as its inverse, consists of successive transformations of each triangular face, by dilatation or compression along an edge, then along the transformed base and along its orthogonal, and finally a rotation, Let us transform first each perspective face of Figure 1 into a 2D view by the use of an inverse 3D Building operation. The three-dimensional perspective of Figure 1 becomes a flat view in Figure 2. However, because of limited software, these successive transformations significantly alter the image quality even if we still distinguish the presence of bands.
We can also directly change the contrast and brightness of each pyramid face of Figure 1 and then assembly the results. The result is better than that given in Figure 2. One clearly sees bands in Western and Southern faces of Figure 3.
The Petrie sequence observed by Satellite photos
Figure 3 shows evidence of bands of unequal width, unequal contrast or brightness. Perhaps this is due to stones from different quarries. But a careful examination of the Petrie sequence of thick stones, labelled as a, b, c, d .. , shows that they correspond to sharp lines of the band edges in the West and South. Various combinations of intermediate stones layers between these thick layers can explain the difference of contrast and brightness.
Petrie (1892) reported the thicknesses of visible layers of stones, which vary from 0.50 m to 1.5 m (at the foot). The 35th layer (label b) has 1.25 m thick. Since he reported the thickness of each layer in abscissa as function of its number in ordinate (N°202 for the top at 138 m), there may be a little mismatch between the position of thick layers in the medallion with their true position in the pyramid. Globally, the correspondence between bands and the Petrie sequence seems to be good. These results highly suggest the existence of degrees and horizontal degree cornices. Thick layers a, b, c, d.. would be used for updating the horizontal level of cornices and also for the foundation of degree walls, as suggested in Chaper III, to reinforce the building. Degree wall heights would not be constant. It raises the question on how the “constraints” revealed by Satellite observations, Petrie’s work (1892) and our microgravity measurement results can be respected by theories on the Cheops pyramid construction: Goyon (1977), Holscher (1912) or Borchardt (1922), Guerrier (1981, 2006), Houdin (2002) or Skillern (2012)? Skillern’s paper presents a theory which might overcome some difficulties related to the outgrowth of stones in horizontal cornice theories (K. R. Skillern, New Satellite Perspectives on Egypt’s Great Pyramids - With A Twist. The Significance of Exposed Rock Bands to Deduction of Exterior Construction Techniques, Private communication, to appear. The author’s email: email@example.com). According to him, thick stones would be put in a horizontal layer after the achievement of the main work, by the completion of the cornice, backwards. He considered two intertwined ramps of 3.5 m width, whirling around the pyramid along inclined cornices of very low slope 2.2%. The “screw dislocation” height corresponds to the degree wall would be hidden by the infillings and coatings. His theory is another version of D. Duham’s model with four intertwined ramps (“Building an Egyptian Pyramid”, Archaeology, 9, 1956). A maquette of his “four ramps”, each ramp starting at a corner, is displayed in the Science Museum of Boston.
Finally, what theory to be considered? I don’t know.
Definitely the Cheops pyramid will keep its mystery for long time.