The variety of generalizations of the Ptolemy's theorem
N. S. Astapovab, I. S. Astapovc
a Novosibirsk State University
b Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c Lomonosov Moscow State University, Institute of Mechanics
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.
area of an arbitrary quadrilateral, equihedral tetrahedron, tetron theorem, Bretschneider theorem, Ptolemy's inequality, Brahmagupta's inequality.
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MSC: Primary 52A38; Secondary 52A40
N. S. Astapov, I. S. Astapov, “The variety of generalizations of the Ptolemy's theorem”, Dal'nevost. Mat. Zh., 19:2 (2019), 129–137
Citation in format AMSBIB
\by N.~S.~Astapov, I.~S.~Astapov
\paper The variety of generalizations of the Ptolemy's theorem
\jour Dal'nevost. Mat. Zh.
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