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A new look at the Egyptian pyramids from the camel of the
21st century.
A. Yurkin
The pictures of pyramids are taken from Internet. Many thanks for authors of these pictures.
The usual pyramid, for example, the Cheops pyramid in Egypt, or the pyramid on a one-dollar bill of the
USA, is half the geometric Plato figure of the octahedron. Moreover, all the pyramids shown in the figures
are made up of large stones of cubic shape.
However, in accordance with the theory of the great German mathematician Felix Klein, the Octahedron
(consisting of two pyramids) is dual to the cube.
In our constructions, our octahedron also consists of small cubes, as well as the Cheops pyramid, but all the
cubes that make up our octahedron are rotated 45 degrees relative to the base of the octahedron
(pyramid). This is the main difference. In our constructions, the octahedron is indeed dual to the cube.
REFERENCES
1) Ahmad MZ, Peters JF. 2019. Proximity induced by order relations. arXiv, 1903.05532v2, 1-22.
2) Askar’yan G, Yurkin A. 1989. New developments in optoacoustics. Sov. Phys. Usp. 32 (4):349 – 356.
3) Almgren FJ Jr, Thurston WP. 1977. Examples of Unknotted Curves Which Bound Only Surfaces of High
Genus Within Their Convex Hulls. Annals of Mathematics. Second Series, Vol. 105(3):527-538. DOI:
10.2307/1970922
4) Bañados E, Venemans BP, Mazzucchelli C, Farina EP, Walter F, et al. 2018. An 800-million-solar-mass black
hole in a significantly neutral Universe at a redshift of 7.5. Nature, 553, 473–476.
5) Brothers HJ. 2012. Finding e in Pascal's triangle. Mathematics Magazine, 85: 51.
doi:10.4169/math.mag.85.1.51
6) de Arcangelis L, Herrmann HJ. 2010.Learning as a phenomenon occurring in a critical state. PNAS 107: 3977-
3981.
7) Edwards AWF. 2013. The arithmetical triangle. In Wilson, Robin; Watkins, John J., Combinatorics: Ancient
and Modern, Oxford University Press, pp. 166–180.
8) Fedotov S, Korabel N. 2015. Nonlinear and non-Markovian random walk: self-organized anomaly.
arXiv:1505.02625v1.
9) Feldman J, Knörrer H, Trubowitz E. 1996. Infinite Genus Riemann Surfaces, Toronto 1995.in Canadian
Mathematical Society/ Société mathématique du Canada 1945-1995. Volume/Tome 3. Edited by James B.
Carrell and Ram Murty, Canadian Mathematical Society, Ottawa (1996) 91-112.
10) Fraiman D, Chialvo DR. 2012. What kind of noise is brain noise: Anomalous scaling behavior of the resting
brain activity fluctuations. Frontiers in Physiology, 3 JUL(July), 1–11. http://doi.org/10.3389/fphys.2012.00307
11) Friston K, Ao P. 2012. Free energy, value, and attractors. Comput Math Methods Med. 2012:937860. doi:
10.1155/2012/937860.
12) Haider B, Duque A, Hasenstaub AR, McCormick DA. 2006. Neocortical network activity in vivo is generated
through a dynamic balance of excitation and inhibition. J Neurosci. 26(17):4535-45.Hemberger M, Shein-
Idelson M, Pammer L, Laurent G. Reliable Sequential Activation of Neural Assemblies by Single Pyramidal
Cells in a Three-Layered Cortex. Neuron. OI:https://doi.org/10.1016/j.neuron.2019.07.017.
13) Hodge RD, Bakken TE, Miller JA, Smith KA, Barkan ER, et al. 2019. Conserved cell types with divergent
features in human versus mouse cortex. Nature;573(7772):61-68. doi: 10.1038/s41586-019-1506-7.
14) Hore PJ. 1983. Solvent suppression in Fourier transform nuclear magnetic resonance. Journal of Magnetic
Resonance, 55 (2): 283–300. doi:10.1016/0022-2364(83)90240-8.
15) Hosokawa T, Yorke HW, Inayoshi K, Omukai K., Yoshida N. 2013. Formation of primordial supermassive
stars by rapid mass accretion. Astrophys J 778, 178.
16) Kaczynski, T., Mischaikov, K., Mrozek, M. 2004. Computational Homology. Springer-Verlag, NY, ISBN 0-
387-40853-3.
17) Kavalali ET, Chung C, Khvotchev M, Leitz J, Nosyreva E, Raingo J, Ramirez DM. Spontaneous
neurotransmission: an independent pathway for neuronal signaling? Physiology (Bethesda). 2011
Feb;26(1):45-53. doi: 10.1152/physiol.00040.2010.
18) Klatt MA, Lovrić J, Chen D, Kapfer SC, Schaller FM, et al. 2019. Universal hidden order in amorphous
cellular geometries. Nature Communications, 10:811.
19) Klein F. 1956. About so-called non-Euclidean geometry. About the geometry bases. Collection of classical
works on Lobachevsky's geometry and development of its ideas. Moscow: Gosizdat.
20) Kolmogorov A, Zhurbenko I, Prokhorov A. 1995. Introduction to the theory of probability. Moscow: Nauka.
21) Krueger C, Garvan C. 2014. Emergence and retention of learning in early fetal development. Infant Behav
Dev, 37(2):162-73. doi: 10.1016/j.infbeh.2013.12.007.
22) Manschot, J., Pioline, B., Sen, A. 2012. From black holes to quivers. High Energy Physics
doi:10.1007/JHEP11(2012)023.
23) Xu X, Wang R. 2014. Neurodynamics of up and down transitions in a single neuron.CognNeurodyn. 8(6):509-
15. doi: 10.1007/s11571-014-9298-9.
24) Peters JF. 2018. Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly
overlapping homology cell complexes. Journal of Mathematical Sciences and Modelling 1, no. 2, 80-85. ISSN
2636-8692.
25) Peters JF. 2019. Computational Geometry, Topology and Physics. Shape Complexes, Optical Vortex Nerves
and Proximities in Digital Images. Springer Int. Pub., 2019, in press.
26) Sarkar J, Maiti SI. 2017. Symmetric Random Walks on Regular Tetrahedra, Octahedra, and Hexahedra.
Calcutta Statistical Association Bulletin (2017) 69(1) 110–128.
27) Soldatov R, Kaucka M, Kastriti ME, Petersen J, Chontorotzea T, et al. 2019. Spatiotemporal structure of cell
fate decisions in murine neural crest. Science, 364(6444). pii: eaas9536. doi: 10.1126/science.aas9536.
28) Sommerfeld A. 1973. Cognition Ways in Physics. Collection of papers, p. 157. Editor: Smorodinsky J.
Moscow: Nauka. (Klein, Riemann und die mathematische Physik. Naturwiss (1919), 7.
29) Telley L, Agirman G, Prados J, Amberg N, Fièvre S, et al. 2019. Temporal patterning of apical progenitors
and their daughter neurons in the developing neocortex. Science.;364(6440). pii: eaav2522. doi:
10.1126/science.aav2522.
30) Tognoli E, Kelso JS. 2013. On the Brain’s Dynamical Complexity: Coupling and Causal Influences Across
Spatiotemporal Scales. Advances in Cognitive Neurodynamics (III), (Iii), 259–265. http://doi.org/10.1007/978-
94-007-4792-0
31) Tozzi A, Zare M, Benasich AA. 2016. New Perspectives on Spontaneous Brain Activity: Dynamic Networks
and Energy Matter. Front Hum Neurosci. 10:247. doi: 10.3389/fnhum.2016.00247.
32) Tozzi A, Peters JF, Fingelkurts AA, Fingelkurts AA, Marijuán PC. 2017. Topodynamics of metastable brains.
Physics of Life Reviews, 21, 1-20. http://dx.doi.org/10.1016/j.plrev.2017.03.001.
33) Tripathy R, Leca I, van Dijk T, Weiss J, van Bon BW, et al. 2018. Mutations in MAST1 Cause Mega-Corpus-
Callosum Syndrome with Cerebellar Hypoplasia and Cortical Malformations. Neuron, 100(6):1354-1368.
DOI:https://doi.org/10.1016/j.neuron.2018.10.044.
34) Trujillo CA , Gao R, Negraes PD, Yeo GW, Voytek B, Muotri AR. 2019. Complex Oscillatory Waves
Emerging from Cortical Organoids Model Early Human Brain Network Development. Cell Stem Cell, 25
(4):558-569.E7. DOI:https://doi.org/10.1016/j.stem.2019.08.002
35) Velasco S, Kedaigle AJ, Simmons SK, Nash A, Rocha M, et al. Individual brain organoids reproducibly form
cell diversity of the human cerebral cortex. Nature, 570, pages523–527.
36) Venemans BP, Walter F, Decarli R, Bañados E, Carilli C, et al. 2017. Copious Amounts of Dust and Gas in a
z = 7.5 Quasar Host Galaxy. The Astrophysical Journal Letters, 851 (1).
37) Veneziano G. 1998. A Simple/Short Introduction to Pre-Big-Bang Physics/Cosmology. arXiv:hep-
th/9802057v2
38) Yurkin A. 1995. System of rays in lasers and a new feasibility of light coherence control. (1995) Optics
Communications, v.114, p. 393.
39) Yurkin A. 2013. New binomial and new view on light theory. About one new universal descriptive geometric
model. (2013) Lambert Academic Publishing, ISBN 978-3-659-38404-2.
40) Yurkin A. 2016. Оn descriptive geometrical interpretation of the principle of Pauli, elements of the table of
Mendeleyev and the Newtonian laminar current of liquid. (2016) Progress in physics, 12: 149-169.
41) Yurkin A. 2018. And where are fluctuations in quantum-mechanical wave function? Advances in Theoretical
& Computational Physics, v. 1. Issue 1.1 -7.
42) Yurkin A, Tozzi A, Peters JF, Marijuán P. 2017. Quantifying Energetic Dynamics in Physical and Biological
Systems Through a Simple Geometric Tool and Geodetic Curves. Progress in Biophysics and Molecular
Biology 131: 153-161.
43) Yurkin A, Peters JF, Tozzi A. 2018. A novel belt model of the atom, compatible with quantum dynamics.
Journal of Scientific and Engineering Research 5(7):413-419. www.jsaer.com.
44) A Yurkin. 2019. Computing Stiks against Random Walk (2019) Advances in Theoretical & Computational
Physics, v. 2. Issue 1.1 -6.
45) Yuste R, Jason N. MacLean, Jeffrey Smith & Anders Lansner. The cortex as a central pattern generator.
Nature Reviews Neuroscience 6, 477-483 (June 2005) | doi:10.1038/nrn1686.
46) Wang Y, Wang R, Zhu Y. 2017. Optimal path-finding through mental exploration based on neural energy
field gradients. CognNeurodyn. 11(1):99-111. doi: 10.1007/s11571-016-9412-2.
47) Wang R, Fan Y, Wu Y. 2019. Spontaneous electromagnetic induction promotes the formation of economical
neuronal network structure via self-organization process. Sci Rep; 9(1):9698. doi: 10.1038/s41598-019-46104-
z.
48) Weyl H. 1955. The Concept of a Riemann Surface, trans. By G.R. MacLane, Dover Pub. Inc., NY, 191 pp.
49) Wise JH, Regan JA, O’Shea BW, Norman ML, Downes TP, Xu H. 2019. Formation of massive black holes
in rapidly growing pre-galactic gas clouds. Nature, 566, 85–88.