6 papers
Cylinder-like Pappus's hexagon theorem in Nil geometry
JenÅ 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…
Power with Respect to Generalized Spheres and Radical Surfaces in
Ãron Világi, JenÅ 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…
Desargues's and Pappus's hexagon theorems on translation-type surfaces in Thurston geometries
JenÅ 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…
Lattice-like Packings and Coverings with Congruent Translation Balls and Cylinders in Sol geometry
Judit Sajtos, JenÅ Szirmai
The aim of this paper is to study lattice-like coverings with congruent translation balls and the packings and coverings with a type of translation cylinders in Sol space related t…
Optimal Horoball Packing Densities for Koszul-type tilings in Hyperbolic -space
Robert T. Kozma, JenÅ Szirmai
We determine the optimal horoball packing densities for Koszul-type Coxeter simplex tilings in hyperbolic -space. Using a parametrization of horoballs by the Busemann function a…
Decomposition method and upper bound density related to congruent saturated hyperball packings in hyperbolic space
Arnasli Yahya, JenÅ Szirmai
In this paper, we study the problem of hyperball (hypersphere) packings in -dimensional hyperbolic space (). We prove that to each -dimensional congruent saturated h…