Geodesic
Mathematics and the Pythagorean theorem in Egypt of the 3rd millennium BC
Matematičeskoe obrazovanie, no. 2 (2024), pp. 69-80 
A. N. Kovalev. Mathematics and the Pythagorean theorem in Egypt of the 3rd millennium BC. Matematičeskoe obrazovanie, no. 2 (2024), pp. 69-80. http://geodesic.mathdoc.fr/item/MO_2024_2_a8/
@article{MO_2024_2_a8,
     author = {A. N. Kovalev},
     title = {Mathematics and the {Pythagorean} theorem in {Egypt} of the 3rd millennium {BC}},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {69--80},
     year = {2024},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2024_2_a8/}
}
TY  - JOUR
AU  - A. N. Kovalev
TI  - Mathematics and the Pythagorean theorem in Egypt of the 3rd millennium BC
JO  - Matematičeskoe obrazovanie
PY  - 2024
SP  - 69
EP  - 80
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MO_2024_2_a8/
LA  - ru
ID  - MO_2024_2_a8
ER  - 
%0 Journal Article
%A A. N. Kovalev
%T Mathematics and the Pythagorean theorem in Egypt of the 3rd millennium BC
%J Matematičeskoe obrazovanie
%D 2024
%P 69-80
%N 2
%U http://geodesic.mathdoc.fr/item/MO_2024_2_a8/
%G ru
%F MO_2024_2_a8

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

New results from an analysis of the proportions and sizes of some pyramids are presented that support the conclusion that the Egyptians most likely knew the Pythagorean theorem back in the 3rd millennium BC. A step-by-step path for the discovery of this theorem is proposed, based on the evolution of ancient Egyptian methods of proportioning in architecture.

[1] Vseobschaya istoriya arkhitektury, V 12 t., v. I, Arkhitektura drevnego mira, Izd. 2-e, ispr. i dop., Stroiizdat, M., 1970, 512 pp.

[2] V. Zamarovskii, Ikh velichestva piramidy, Nauka, M., 1981

[3] G. A. Zverkina, “Algoritm Evklida kak vychislitelnoe sredstvo antichnoi matematiki”, Istoriko-matematicheskie issledovaniya, 2000, no. 5 (40), 232–243 | MR | Zbl

[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] 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, Chast II”, Matematicheskoe obrazovanie, 2023, no. 105, 54–66

[7] A. I. Schetnikov, “Zolotoe sechenie, kvadratnye korni i proportsii piramid v Gize”, Matematicheskoe obrazovanie, 2006, no. 3 (38), 59–71

[8] D. Fowler, E. Robson, “Square Root Approximations in Old Babylonian Mathematics: YBC 7289 in Context”, Historia Mathematica, 25:4 (1998), 366–378 | DOI | MR | Zbl

[9] Hirsch Antoine Pierre, Ancient Egyptian Cubits — Origin and Evolution, PhD thesis, Toronto, 2013

[10] Irigaray Christian, The Pyramids of Sneferu, Montevideo, 2020

[11] V. Maragioglio, C. Rinaldi, L’architettura delle Piramidi Memfite, Parte III, Il Complesso di Meydum, la piramide a Doppia Pendenza e la piramide Settentrionale in Pietra di Dahsciur, Artale, Torino, 1964

[12] V. Maragioglio, C. Rinaldi, L’architettura delle Piramidi Menfite, Parte IV,. Le Grande Piramide di Cheope, Artale, Torino, 1965

[13] Richard A. Parker, Demotic Mathematical Papyri, Brown University Press, Providence, R.I.; Humphries, London, 1972 | Zbl

[14] C. Rossi, “Note on the Pyramidion Found at Dahshur”, JEA, 1999, no. 85, 219–222

[15] C. Rossi, Architecture and mathematics in Ancient Egypt, Cambridge University press, 2003