The Great Pyramid has the character of concavity that each of its four faces is slightly indented along its central line. Applying the geometry on an inclined plane, we show that this concavity could be derived from its inner structure of inward sloping courses gently inclined towards the center of each course, at about 11 degrees to the horizontal, i.e., the slope 1/5 by the ratio of “rise over run”. We explain why the inclined layers together with the reinforced base were necessary for the long-term stability of the Pyramid against the severe natural forces like the high gravitational compression, earthquakes and rainstorms, pointing out the feasible fact that the Pyramid has experienced severe rainstorms more than 500 times during the 4500 years. The crucial point about stability is that the effects of such natural forces are quite different between the core of inclined courses and that of truly level courses in the sense that the former can be tightened to become stronger over time, but the latter would be disintegrated to be weaker over time. Scaled-down models of the Pyramid are introduced to understand the large-scale dynamics of the Pyramid. In particular, the small model reduced by 10-3 helps us to imagine the transformation of vertical into lateral forces, pointed out by Mendelssohn. On the other hand, the Step Pyramid of Djoser can be identified almost as the half-sized model of the Great Pyramid when the Great Pyramid was assumed to be composed only of truly level courses. And this identification tells the fate of the Great Pyramid only of truly level courses that it would have almost collapsed until now like the Step Pyramid before the recent restoration.
References
[1]
Alharbi, M. M. E. A. (2018). Analysis of Extreme Precipitation Events over the Eastern Red Sea Coast for Recent and Future Climate Conditions. Ph.D. Thesis, University of Birmingham.
[2]
Andrade, F. O. (1992). La construcción en Egipto. Primera Parte. Re. Revista de Edificación, 10, 55-65. https://doi.org/10.15581/020.10.35028
[3]
Arnold, D. (1991). Building in Egypt, Pharaonic Stone Masonry. Oxford University Press.
[4]
Badawy, A. (1999). Historical Seismicity of Egypt. Acta Geodaetica et Geophysica Hungarica, 34, 119-135.
[5]
Bauval, J. P. (2016). The Concavity of the Great Pyramid: A Design Feature? Did the Designer Know the Meter Unit? https://www.academia.edu/27553148
[6]
Bell, B. (1975). Climate and the History of Egypt: The Middle Kingdom. American Journal of Archaeology, 79, 223-269. https://doi.org/10.2307/503481
[7]
Biondi, F., & Malanga, C. (2022).Synthetic Aperture Radar Doppler Tomography Reveals Details of Undiscovered High-Resolution Internal Structure of the Great Pyramid of Giza. Remote Sensing, 14, Article No. 5231. https://doi.org/10.3390/rs14205231
[8]
Butzer, K. W., Butzer, E. B., & Love, S. (2013). Urban Geoarchaeology and Environmental History at the Lost City of the Pyramids, Giza: Synthesis and Review. Journal of Archaeological Science, 40, 3340-3366. https://doi.org/10.1016/j.jas.2013.02.018
[9]
Cacciola, P., Shadlou, M., Ayoub, A., Rashed, Y. F., & Tombari, A. (2022). Exploring the Performances of the Vibrating Barriers for the Seismic Protection of the Zoser Pyramid. Scientific Report, 12, Article No. 5542. https://doi.org/10.1038/s41598-022-09444-x
[10]
Creighton, S., & Osborn, G. (2008). The Great Pyramid and the Axis of the Earth—Part 2. Graham Hancock. https://grahamhancock.com/creightons4/
[11]
Dash, G., & Paulson, J. (2015). The 2015 Survey of the Base of the Great Pyramid. The Journal of Egyptian Archaeology, 102, 186-196. https://www.academia.edu/36742756 https://doi.org/10.1177/030751331610200114
[12]
De Vries, A. J., Tyrlis, E., Edry, D., Krichak, S. O., Steil, B., & Lelieveld, J. (2013). Extreme Precipitation Events in the Middle East: Dynamics of the Active Red Sea Trough. Journal of Geophysical Research: Atmospheres, 118, 7087-7108. https://doi.org/10.1002/jgrd.50569
[13]
Deus, H. M., Bolacha, E., Vasconcelos, C., & Fonseca, P. E. (2010) Analogue Modelling to Understand Geological Phenomena. In Proceedings of the GeoSciEd VI. University of Witwatersrand. https://www.researchgate.net/publication/266375082
[14]
Edwards, J. F. (2016). The Concave Faces of the Great Pyramid: An Explanation. Technology and Culture, 57, 909-925. https://doi.org/10.1353/tech.2016.0111
[15]
Ewais, A. Y., Ahmed, M. A., & Faried, M. (2016). A Close Look at the Step Pyramid Restoration Project, JCHC 4.
[16]
Groves, P. R. C., & McCrindle, J. R. (1926). Flying over Egypt, Sinai, and Palestine, In The National Geographic Magazine 1926-09 (Vol. 10, No. 3, pp. 312-355). National Geographic. https://www.scribd.com/document/46834946/National-Geographic-1926-09
[17]
Hawass, Z. (1996). The Discovery of the Satellite Pyramid of Khufu (G1-d). In P. Der Manuelian (Ed.), Studies in Honor of William Kelly Simpson (pp. 379-398). Museum of Fine Arts.
[18]
Hemeda, S., & Sonbol, A. (2020). Sustainability Problems of the Giza Pyramids. Heritage Science, 8, Article No. 8. https://doi.org/10.1186/s40494-020-0356-9
[19]
Hubbert, M. K. (1937). Theory of Scale Models as Applied to the Study of Geologic Structures. Geological Society of America Bulletin, 48, 1459-1520. https://doi.org/10.1130/GSAB-48-1459
[20]
Isler, M. (1983). Concerning the Concave Faces of the Great Pyramid. Journal of the American Research Center in Egypt, 20, 27-32. https://doi.org/10.2307/40000899
[21]
Isler, M. (2001). Sticks, Stones, and Shadows: Building the Egyptian Pyramids. University of Oklahoma Press.
[22]
Kato, A. (2020). How They Moved and Lifted Heavy Stones to Build the Great Pyramid. Archaeological Discovery, 8, 47-62. https://doi.org/10.4236/ad.2020.81003
[23]
Khalil, A. E., Hafiez, H. E. A., Girgis, M., & Taha, M. A., (2017). Earthquake Ground Motion Simulation at Zoser Pyramid Using the Stochastic Method: A Step toward the Preservation of an Ancient Egyptian Heritage. NRIAG Journal of Astronomy and Geophysics, 6, 52-59. https://doi.org/10.1016/j.nrjag.2016.11.003
[24]
Kukela, A., & Seglins, V. (2013). Assessment of Stone Material Deterioration of the Exposed Surfaces of the Step Pyramid in Saqqara. Journal of Earth Science and Engineering, 3, 238-244.
[25]
Mendelssohn, K. (1971). A Scientist Looks at the Pyramids: Engineering Evidence Connected with the Building of the Great Pyramids Suggests Conclusions That Go Far beyond the Problems of Pyramid Design. American Scientist, 59, 210-220.
[26]
Mendelssohn, K. (1973). A Building Disaster at the Meidum Pyramid. The Journal of Egyptian Archaeology, 59, 60-71. https://doi.org/10.1177/030751337305900108
[27]
Mendelssohn, K. (1976). The Riddle of the Pyramids. Thames & Hudson.
[28]
Merle, O. (2015). The Scaling of Experiments on Volcanic Systems. Frontiers in Earth Science, 3, Article 26. https://doi.org/10.3389/feart.2015.00026
[29]
Monnier, F. (2022). The So-Called Concave Faces of the Great Pyramid. Interdisciplinary Egyptology, 1, 1-18.
[30]
Morsy, S. W., & Halim, M. A., (2015). Reasons Why the Great Pyramids of Giza Remain the Only Surviving Wonder of the Ancient World: Drawing Ideas from the Structure of the Giza Pyramids to Nuclear Power Plants. Journal of Civil Engineering and Architecture, 9, 1191-1201. https://doi.org/10.17265/1934-7359/2015.10.007
[31]
Ogilvie-Herald, C. (2020). Climate Change and the Age of the Great Sphinx. https://www.academia.edu/43952795/
[32]
Petrie, W. M. F. (1883). The Pyramids and Temples of Gizeh. Histories & Mysteries of Man Ltd.
[33]
Pochan, A. (1971). L’énigme de la grande pyramide. Robert Laffont.
[34]
Pollard, D. D., & Fletcher, R. C. (2005). Fundamentals of Structural Geology. Cambridge University Press.
[35]
Raynaud, S., de La Boisse, H., Makroum, F. M., & Bertho, J. (2008). Geological and Geomorphological Study of the Original Hill at the Base of Fourth Dynasty Egyptian Monuments. HAL ID: hal-00319586. HAL.
[36]
Ritner, R. K., & Moeller, N. (2014). The Ahmose “Tempest Stela”, Thera and Comparative Chronology. Journal of Near Eastern Studies, 73, 1-19. https://doi.org/10.1086/675069 http://www.jstor.org/stable/10.1086/675069
[37]
Schellart, W. P., & Strack, V. (2016). A Review of Analogue Modelling of Geodynamic Processes: Approaches, Scaling, Materials and Quantification, with an Application to Subduction Experiments. Journal of Geodynamics, 100, 7-32. https://doi.org/10.1016/j.jog.2016.03.009
[38]
Seyfzadeh, M. (2017). The Mysterious Pyramid on Elephantine Island: Possible Origin of the Pyramid Code. Archaeological Discovery, 5, 187-223. https://doi.org/10.4236/ad.2017.54012
[39]
Seyfzadeh, M. (2018a). Essential Design of the Great Pyramid Encoded in Hemiunu’s Mastaba at Giza. Archaeological Discovery, 6, 162-172. https://doi.org/10.4236/ad.2018.62008
[40]
Seyfzadeh, M. (2018b). Hemiunu Used Numerically Tagged Surface Ratios to Mark Ceilings inside the Great Pyramid Hinting at Designed Spaces Still Hidden within. Archaeological Discovery, 6, 319-337. https://doi.org/10.4236/ad.2018.64016
[41]
Weeks, K.R. (1995). The Work of the Theban Mapping Project and the Protection of the Valley of the Kings. In R. H. Wilkinson (Ed.), Valley of the Sun Kings (pp. 122-128). University of Arizona Egyptian Expedition.
[42]
Yasseen, A. (2018) Architecture of the Great Pyramid of Giza Concept and Construction. Proceedings of Science and Technology, 1, 97-108,
[43]
Zalewski, F. (2017). Petrographic Observations of the Building Stones of the Great Pyramid of Giza. Journal of Geological Resource and Engineering, 4, 153-168.
