2013/01/29 by Géza Csima, Csima, Géza, Jenő Szirmai +1
Engineering · Mathematics · #14H50 #51F05 #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications #Metric Geometry (math.MG) #math.GT #math.MG #msc:14H50 #msc:51F05
paper · pdf · doi:10.48550/arxiv.1301.6991
openalex publication_date 2013/01/29 · arxiv created 2013/01/30 · arxiv updated 2013/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper we consider the isoptic curves on the 2-dimensional geometries of constant curvature \bE2,~\bH2,~\cE2. The topic is widely investigated in the Euclidean plane \bE2 see for example \citeCMM91 and \citeWi and the references given there, but in the hyperbolic and elliptic plane there are few results in this topic (see \citeCsSz1 and \citeCsSz2). In this paper we give a review on the preliminary results of the isoptics of Euclidean and hyperbolic curves and develop a procedure to study the isoptic curves in the hyperbolic and elliptic plane geometries and apply it for some geometric objects e.g. proper conic sections. We use for the computations the classical models which are based on the projectiv interpretation of the hyperbolic and elliptic geometry and in this manner the isoptic curves can be visualized on the Euclidean screen of computer.