From equality of Pythagoras to equality of Ptolemy
Matematičeskoe obrazovanie, no. 1 (2021), pp. 2-4
Cet article a éte moissonné depuis la source Math-Net.Ru
For a quadrilateral inscribed in a circle, the connection between Ptolemy's equality and the equality of Pythagoras is noted. A formula is obtained for the ratio of the diagonals of the quadrilateral, the lengthes of the diagonals are determined.
@article{MO_2021_1_a0,
author = {V. K. Gavrilov},
title = {From equality of {Pythagoras} to equality of {Ptolemy}},
journal = {Matemati\v{c}eskoe obrazovanie},
pages = {2--4},
year = {2021},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MO_2021_1_a0/}
}
V. K. Gavrilov. From equality of Pythagoras to equality of Ptolemy. Matematičeskoe obrazovanie, no. 1 (2021), pp. 2-4. http://geodesic.mathdoc.fr/item/MO_2021_1_a0/
[1] Ya. P. Ponarin, Elementarnaya geometriya, v. 1, MTsNMO, M., 2004
[2] S. A. Anischenko, Lektsii po geometrii, v. 1, Izdatelstvo KGPU, Krasnoyarsk, 1988
[3] , 2012 https://nashaucheba.ru/v7370/referat-Teorema Ptolemeya-fail n1.doc
[4] A. P. Kiselev, Geometriya, ed. N. A. Glagolev, FIZMATLIT, M., 2004
[5] Yu. V. Prokhorov (gl. red.), BES Matematika, “Bolshaya Rossiiskaya entsiklopediya”, M., 1998
[6] V. K. Gavrilov, “Ot ravenstva Pifagora k ravenstvu Ptolemeya”, Informatsionnye tekhnologii v matematike i matematicheskom obrazovanii, Materialy VII Vserossiiskoi nauchno-metodicheskoi konferentsii s mezhdunarodnym uchastiem (Krasnoyarsk, 2018), 87–89