vendredi 2 mai 2008

Kheops Pyramid

My interest in the Kheops Pyramid dated about twenty years ago. At this time (1987), working at EDF on inverse problems for the assessment of nuclear structures, my Director Marc Albouy asked me to supervise a study on the Kheops Pyramid for searching an unknown tomb of the Pharaon, from microgravity measurements. At this time, two French architects, G. Dormion and J.P. Goidin remarked some architectural details of the tunnel walls which should hide some cavity behind, may be an unknown tomb of the Pharaon? It was a fantastic challenge for all of us to work on the Great Pyramid, which was more exciting than to detect a dangerous flaw in a nuclear vessel !
As a sponsor for scientifc works devoted to archeology, EDF granted financial supports to the French Company of Geophysical Prospection (CPGF) for microgravity measurements, done by Jacques Lashkmanan and his team. I was in charge of the mathematical and numerical team at EDF for the inversion of measurements in order to obtain the density distribution near the tunnels. The result obained for the unknown tomb was rather negative. What a disappointment to all of us.
We then decided to modellize the entire Pyramid with regular meshes and to look at the density distribution. The results for the second study are very interesting. First of all, we found that the pyramid has a high density about 2.4 near its base and a very low one at the top, about 1.87. Second, the misfit of density presents some special structure. In the Proceedings of the International Symposium : "The Engineering Geology of Ancient Works, Monuments and Historical Sites", The Application of microgravity survey in the endoscopy of ancient monuments by H.D. Bui, J. Montlucon, J. Lahksmanan, J.C. Erling, C. Nakla, pp. 1063-1069, Athens 19-23 September, 1988, Marinos & Koulis (Balkema, Rotterdam), we wrote in the conclusion : ".. the Pyramid density does not present a simple symmetry other than a certain spiral structure". An altogether incredible story is that in 2002, Henri Houdin (Engineer) and his son Jean-Pierre Houdin (architect) proposed a new theory on the construction of the Kheops Pyramid which should involve an internal tunnel spiraling up counterclockwise, exactly as given in our numerical result (1988) !

For more information about Houdin's theory, see:

The densitogram represents the mean density distribution on the surface of the Pyramid over 10m thick at the bottom, 3-4 m at the top. It has been worked out in 1988 by H.D. Bui (EDF), J. Lakshmanan (CPGF) and coworkers. It is the property of Fondation EDF. (Copyright EDF free, additional drawings to the image not authorized)

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