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math.MG2026
Cylinder-like Pappus's hexagon theorem in Nil geometry
Jenő Szirmai
In this paper we deal with Nil geometry, in whose projective model the geodesic curves are helix-like and fit onto geodesic Nil cylinders of revolution with fibrum axes. In this pa…
math.MG2026
Power with Respect to Generalized Spheres and Radical Surfaces in
Áron Világi, Jenő Szirmai
This paper presents a unified theory for the power of a point with respect to generalized spheres (spheres, horospheres, and hyperspheres) in -dimensional hyperbolic space $\mat…
math.MG2026
Desargues's and Pappus's hexagon theorems on translation-type surfaces in Thurston geometries
Jenő Szirmai
In \cite{Sz25} we generalized the famous Menelaus' and Ceva's theorems for translation triangles in each non-constant curvature Thurston geometry. In this paper based on the descri…