Geodesic
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, Tome 105 (2023) no. 1, pp. 54-66.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is hypothesized that in the Old Kingdom, after finding the fraction 47/21 for $\sqrt{5}$, discovered by Shchetnikov when analyzing the proportions of the burial chamber of the Great Pyramid, an inch was introduced as 1/21 of the royal cubit. Examples are given from architecture and religious art in which the inch was used. 
@article{MO_2023_105_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},
     publisher = {mathdoc},
     volume = {105},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2023_105_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
VL  - 105
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MO_2023_105_1_a6/
LA  - ru
ID  - MO_2023_105_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
%V 105
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MO_2023_105_1_a6/
%G ru
%F MO_2023_105_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, Tome 105 (2023) no. 1, pp. 54-66. http://geodesic.mathdoc.fr/item/MO_2023_105_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) <ext-link ext-link-type='uri' href='https://marhi.ru/AMIT/2017/1kvart17/PDF/10_AMIT_38_VENGEROVA_PDF.pdf'>https://marhi.ru/AMIT/2017/1kvart17/PDF/10_AMIT_38_VENGEROVA_PDF.pdf</ext-link>

[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 <ext-link ext-link-type='doi' href='https://doi.org/10.2307/40000070'>10.2307/40000070</ext-link>

[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 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=469613'>469613</ext-link>

[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 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=910500'>910500</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0788.01006'>0788.01006</ext-link>

[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