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- W2613156932 abstract "In the present paper we study the $SOL$ geometry that is one of the eight homogeneous Thurston 3-geomet-ri-es. We determine the equation of the translation-like bisector surface of any two points. We prove, that the isosceles property of a translation triangle is not equivalent to two angles of the triangle being equal and that the triangle inequalities do not remain valid for translation triangles in general. Moreover, we develop a method to determine the centre and the radius of the circumscribed translation sphere of a given {it translation tetrahedron}. In our work we will use for computations and visualizations the projective model of $SOL$ described by E. Molnar in cite{M97}." @default.
- W2613156932 created "2017-05-19" @default.
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- W2613156932 date "2017-05-10" @default.
- W2613156932 modified "2023-10-18" @default.
- W2613156932 title "Bisector surfaces and circumscribed spheres of tetrahedra derived by translation curves in $SOL$ geometry" @default.
- W2613156932 cites W1494599013 @default.
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