|
Mathematical Education, 2020, Issue 2(94), Pages 18–28
(Mi mo699)
|
|
|
|
Students and teachers of secondary school
The modern generalizations of the Ptolemy's theorem
N. S. Astapovab, I. S. Astapovc a Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
c Lomonosov Moscow State University, Institute of Mechanics
Abstract:
The article examines the metric properties of a tetron. In particular case a tetron is a triangle, flat or spatial quadrangle, and also a tetrahedron. The main theorem is proved about the connection of the lengths of the sides, the magnitudes of the plane angles and the magnitude of the dihedral angle of the tetron is proved. Many remarkable theorems about triangles, quadrangles, and tetrahedra are the corollaries of this theorem. Special attention given to equihedral tetrahedra.
Keywords:
tetron, Ptolemy's theorem, triangle, flat and spatial quadrilateral, equilateral tetrahedron.
Citation:
N. S. Astapov, I. S. Astapov, “The modern generalizations of the Ptolemy's theorem”, Math. Ed., 2020, no. 2(94), 18–28
Linking options:
https://www.mathnet.ru/eng/mo699 https://www.mathnet.ru/eng/mo/y2020/i2/p18
|
Statistics & downloads: |
Abstract page: | 192 | Full-text PDF : | 1274 | References: | 18 |
|