Triangle angle sums related to translation curves in \SOL geometry

2017/03/20 by Jenő Szirmai, Szirmai, Jenő · 2 citations
Computer Science · Mathematics · Social Sciences · #52C35 #53A20 #53A35 #53B20 #Computational Geometry and Mesh Generation #FOS: Mathematics #Historical Geography and Cartography #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1703.06646

openalex publication_date 2017/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

After having investigated the geodesic and translation triangles and their angle sums in \NIL and \SLR geometries we consider the analogous problem in \SOL space that is one of the eight 3-dimensional Thurston geometries. We analyse the interior angle sums of translation triangles in \SOL geometry and prove that it can be larger or equal than π. In our work we will use the projective model of \SOL described by E. Molnár in \citeM97,

Cited by

• Lattice-like Packings and Coverings with Congruent Translation Balls and Cylinders in Sol geometry
• Menelaus' and Ceva's theorems for translation triangles in Thurston geometries

Related

• Interior angle sums of geodesic triangles and translation-like isoptic surfaces in Sol geometry
• Translation-like isoptic surfaces and angle sums of translation triangles in \NIL geometry
• Interior angle sums of geodesic triangles in S² × R and H² × R geometries
• The sum of the interior angles in geodesic and translation triangles of Sl2(R) geometry
• NIL geodesic triangles and their interior angle sums