Abstract: Conway established the following geometric fact: If the sides AB and AC of a triangle ABC are prolonged beyond the point A by the length of the opposite side BC and the same is done with the vertices B and C, then the so-constructed 6 points lie on the sole circle whose center coincides with the center of the inscribed circle. V.A. Alexandrov found a spatial analog of the Conway circle. Namely, if in a tetrahedron ABCD we mark three points on the prolongations of the edges AB, AC,andAD beyond the vertex A at distance from A to the half-perimeter of the opposite face BCD andthendo the same with the remaining vertices B, C,andD then the so-constructed 12 points lie on the same sphere if and only if ABCD is a frame tetrahedron. We address the multidimensional version of the fact for a simplex in the Euclidean space En.

Cite: Malyugin S.A.
A Multidimensional Analog of the Conway Circle
Siberian Mathematical Journal. 2024. V.65. N4. P.810-817. DOI: 10.1134/s0037446624040086 WOS Scopus РИНЦ OpenAlex

Original: Малюгин С.А.
Многомерный аналог окружности Конвея
Сибирский математический журнал. 2024. Т.65. №4. С.693-701. DOI: 10.33048/smzh.2024.65.408 РИНЦ

Dates:

Submitted:	Jan 16, 2024
Accepted:	Jun 20, 2024
Published print:	Jul 16, 2024
Published online:	Jul 16, 2024

Identifiers:

Web of science:	WOS:001272553600020
Scopus:	2-s2.0-85198634799
Elibrary:	68538181
OpenAlex:	W4400697949

Citing: Пока нет цитирований

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