@article{MO_2023_1_a6,
author = {A. N. Kovalev},
title = {Fractions for $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$, quasi-pythagorean triples and the appearance of the royal cubit, foot and inch in {Egypt} during the {Old} {Kingdom.} {Part} {II}},
journal = {Matemati\v{c}eskoe obrazovanie},
pages = {54--66},
year = {2023},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MO_2023_1_a6/}
}
TY - JOUR
AU - A. N. Kovalev
TI - Fractions for $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$, quasi-pythagorean triples and the appearance of the royal cubit, foot and inch in Egypt during the Old Kingdom. Part II
JO - Matematičeskoe obrazovanie
PY - 2023
SP - 54
EP - 66
IS - 1
UR - http://geodesic.mathdoc.fr/item/MO_2023_1_a6/
LA - ru
ID - MO_2023_1_a6
ER -
%0 Journal Article
%A A. N. Kovalev
%T Fractions for $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$, quasi-pythagorean triples and the appearance of the royal cubit, foot and inch in Egypt during the Old Kingdom. Part II
%J Matematičeskoe obrazovanie
%D 2023
%P 54-66
%N 1
%U http://geodesic.mathdoc.fr/item/MO_2023_1_a6/
%G ru
%F MO_2023_1_a6
A. N. Kovalev. Fractions for $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$, quasi-pythagorean triples and the appearance of the royal cubit, foot and inch in Egypt during the Old Kingdom. Part II. Matematičeskoe obrazovanie, no. 1 (2023), pp. 54-66. http://geodesic.mathdoc.fr/item/MO_2023_1_a6/
[1] M. E. Vengerova, “Reshenie zadachi “kvadratury kruga” v geometricheskom proportsionirovanii drevnerusskikh khramov X–XV vekov”, Architecture and Modern Information Technologies, 2017, no. 1(38) https://marhi.ru/AMIT/2017/1kvart17/PDF/10_AMIT_38_VENGEROVA_PDF.pdf
[2] D.E.Arkin, N.I.Brunov, M.Ya.Ginzburg i dr. (red.), Vseobschaya istoriya arkhitektury, v. I, Izdatelstvo Akademii Arkhitektury SSSR, M., 1944, 370 pp.
[3] Vseobschaya istoriya arkhitektury, V 12 t., v. I, Arkhitektura drevnego mira, Izd. 2-e, ispr. i dop., Stroiizdat, M., 1970, 512 pp.
[4] Istoriya matematiki s drevneishikh vremen do nachala XIX stoletiya, V 3 t., v. 1, Nauka, M., 1970
[5] A. N. Kovalev, “Drobi dlya $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$, kvazipifagorovy troiki i poyavlenie tsarskogo loktya, futa i dyuima v Egipte vremen Drevnego tsarstv”, Matematicheskoe obrazovanie, 2022, no. 102, 43–54
[6] Zh.-F. Lauer, Zagadki egipetskikh piramid, Nauka, M., 1966
[7] A. V. Radzyukevich, Yu. G. Marchenko, “K voprosu o razmerakh i proportsiyakh piramidy Kheopsa”, Vestnik TGASU, 2015, no. 1, 9–22
[8] O. Shuazi, Vseobschaya istoriya arkhitektury. Ot doistoricheskoi epokhi do romanskoi arkhitektury, AST, M., 2019
[9] A. I. Schetnikov, “Zolotoe sechenie, kvadratnye korni i proportsii piramid v Gize”, Matematicheskoe obrazovanie, 2006, no. 3(38), 59–71
[10] R. Arnheim, The Dynamics of Architectural Forms, University of California Press, Berkeley/London, 1977
[11] J. Baines, “Restricted Knowledge, Hierarchy and Decorum: Modern Perceptions and Ancient Institutions”, JARCE, 27 (1990), 1–230 | DOI
[12] J. Bonwick, Pyramid facts and fancies, C. Kegan Paul Co, London, 1877
[13] C. Rossi, “Note on the Pyramidion Found at Dahshur”, JEA, 85 (1999), 219–222
[14] C. Rossi, Architecture and mathematics in Ancient Egypt, Cambridge University press, 2003, 280 pp.
[15] R. J. Gillings, Mathematics at the Time of the Pharaohs, Massachusettes Institute of Technology Press, Cambridge, 1972 | MR
[16] A. P. Hirsch, Ancient Egyptian Cubits – Origin and Evolution, PhD thesis, Toronto, 2013
[17] M. Lehner, The complete pyramids, London, 1997
[18] V. Maragioglio, C. Rinaldi, L’architettura delle Piramidi Menfite, v. IV, Tavole, Torino, 1962
[19] V. Maragioglio, C. Rinaldi, L’architettura delle Piramidi Menfite. Parte IV. Le Grande Piramide di Cheope, Artale, Torino, 1965
[20] V. Maragioglio, C. Rinaldi, C. L’architettura delle Piramidi Menfite, Parte V. Le Piramidi di Zedefra e di Chefren, Canessa, Rapallo, 1966
[21] G. Robins, Ch. Shute, The Rhind Mathematical Papyrus, British Museum Press, London, 1987 | MR | Zbl
[22] E. Unger, “Die Nippur-Elle, Publikationen der Kais. Osman. Museen, Konstantinopel, 1916 ders. - Eberts Reallexikon, Stichwort Nippur”, Elle, VIII (1927), 58 pp.
[23] N. Victor, “The Rod (Nbj) and its use in Egyptian Architecture”, Göttinger Miszellen, 1991, no. 21, 101–110
[24] P. Zignani, Le temple d'Hathor à Dendara: Relevés et étude architecturale, Institut français d'archéologie orientale du Caire, Le Caire, 2010