Geodesic
The modern generalizations of the Ptolemy's theorem
Matematičeskoe obrazovanie, Tome 94 (2020) no. 2, pp. 18-28

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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.
Mots-clés : tetron
Keywords: Ptolemy's theorem, triangle, flat and spatial quadrilateral, equilateral tetrahedron. 
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     author = {N. S. Astapov and I. S. Astapov},
     title = {The modern generalizations of the {Ptolemy's} theorem},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {18--28},
     publisher = {mathdoc},
     volume = {94},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2020_94_2_a1/}
}
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N. S. Astapov; I. S. Astapov. The modern generalizations of the Ptolemy's theorem. Matematičeskoe obrazovanie, Tome 94 (2020) no. 2, pp. 18-28. http://geodesic.mathdoc.fr/item/MO_2020_94_2_a1/