By H. D. Bui
In this e-book Egyptian Archeology and arithmetic meet.
The writer is knowledgeable in theories and purposes in reliable Mechanics and Inverse difficulties, a former professor at Ecole Polytechnique and now works with Electricité de France on upkeep operations on nuclear strength crops. within the Autumn of 1986, after the tip of the operation at the King’s chamber carried out less than the Technological and clinical Sponsorship of EDF, to find a hollow space, he used to be known as to unravel a mathematical inverse challenge, to discover the unknown tomb of the King and the density constitution of the total pyramid in accordance with measurements of microgravity made inside and out of the pyramid.
This booklet recounts many of the seek operations at the pyramid of Cheops made on the request of the Egyptian and French experts in 1986-1987. After the untimely finish of the Cheops operation within the Autumn of 1986, following the fiasco of unsuccessful drillings within the region suspected via either architects G. Dormion and J.P. Goidin and microgravity auscultation, EDF and CPGF (a geophysical corporation) groups endured their researches with measurements already made, making an attempt this time an inversion of the Newton gravity equation for the complete pyramid and utilizing one other theoretical group led by means of the writer. The inverse challenge answer proven the result of auscultations, yet discovered no hollow space. despite the fact that, clone of the common density on the floor of the whole pyramid kinds a type of sq. “spiral” most likely relating to the development strategy. In 2000, Jean-Pierre Houdin thought of the author’s result of 1988 as a affirmation of his concept of the interior ramp tunnel. due to the fact that then the writer has performed extra examine and located that classical theories of the development in accordance with levels and the actual mode of stones filling may also record a similar densitogram. The publication is richly illustrated with colour figures. it's dotted with info bearing on Physics, Mechanics and the historical past of Egyptian Antiquities. The publication ends with the best secret of the pyramid in regards to the unknown tomb of the King and a dream to determine the tomb at an unforeseen place.
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Extra info for Imaging the Cheops Pyramid
Theoretical values of gravity due to the cavity (in Green) are shown in Fig. 9. As expected, one obtains a continuous variation from negative value −30 μGals in Blue, to positive one +30 μGals in Red (there is a lesser attractive force because of a missing mass above the apparatus). Comparing the direct computation, Fig. 9, with measurements, Fig. 3, we see some differences, but we are unable to draw a conclusion on the existence of cavities or not. A direct computation by trials and errors of the geometry and location of a cavity has no chance to get the solution of an inverse problem.
D) is the a priori knowledge, C is some constant for bounding the space of solution, α≥0 is the Tikhonov regularization constant, chosen here arbitrarily, but possibly determined in an optimal manner by Kitagawa’s choice method, (See the reference [Bui, 1993]) and CX et Cb are covariant matrices for weighting the two terms, in general diagonal matrices and positive matrices of rank N and M respectively, introduced for having some range of the solution X and some uncertainty on the measurement b.
E. there is 33% of void (Photo). A compact arrangement of spheres (8) with the same diameter has a weaker √ percentage of void 1 − π/ 18 ≈ 26%. The percentage is smaller when there are different diameters. Therefore there are so many voids between stones, which can be created either by the dissolution of plasters between stones, or simply by existing voids due to irregular shape stones, like disordered cube sugars in our box of Fig. 7. In 1819, G. A. F. Fitzclarence broke into a visible huge cavity near the North-Eastern ridge, about 87 m height, which was called « the fox hole» by our colleague Pierre Deletie when he saw a fox disappearing in the hole.