Geodesic
A Rational Trigonometric Relationship Between the Dihedral Angles of a Tetrahedron and its Circumradius
Journal for geometry and graphics, Tome 24 (2020) no. 2, pp. 207-216.

Voir la notice de l'article provenant de la source Heldermann Verlag

This paper will extend a known relationship between the circumradius and dihedral angles of a tetrahedron in three-dimensional Euclidean space to three-dimensional affine space over a general field not of characteristic two or three, using only the framework of rational trigonometry devised by Wildberger. In this framework, a linear algebraic view of trigonometry is presented, which allows the associated three-dimensional vector space of such a three-dimensional affine space to be equipped with a non-degenerate symmetric bilinear form. This will also generalise the results presented to arbitrary geometries parameterised by such a non-degenerate symmetric bilinear form.
Classification : 51M04, 51N10, 15A63, 11E04
Mots-clés : Rational trigonometry, tetrahedron, circumradius, dihedral angle, symmetric bilinear form 
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     title = {A {Rational} {Trigonometric} {Relationship} {Between} the {Dihedral} {Angles} of a {Tetrahedron} and its {Circumradius}},
     journal = {Journal for geometry and graphics},
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G. A. Notowidigdo . A Rational Trigonometric Relationship Between the Dihedral Angles of a Tetrahedron and its Circumradius. Journal for geometry and graphics, Tome 24 (2020) no. 2, pp. 207-216. http://geodesic.mathdoc.fr/item/JGG_2020_24_2_JGG_2020_24_2_a5/