The orthogonal conics of the elliptic plane
type: Item
instance of: scholarly article
title: The orthogonal conics of the elliptic plane
zbMATH Open document ID: 0874.51009
DOI: 10.1007/BF03322190
author: Herbert Urban
published in: Results in Mathematics
publication date: 1997-11-04T00:00:00Z
review text: In the elliptic plane a conic is called orthogonal, if it contains a special real point \(A\) and the intersecting points of the polar of \(A\) with respect to the absolute conic. The author shows interesting properties of orthogonal conics (an analogon to the theorem of Thales), gives a construction of such conics through 3 and 4 points and applications in elliptic kinematics. Many of the special loci of local elliptic kinematics are orthogonal conics.
Mathematics Subject Classification ID: 51N25
Mathematics Subject Classification ID: 53A17
zbMATH DE Number: 933266
zbMATH Keywords: elliptic plane
zbMATH Keywords: orthogonal conics
reviewed by: Otto Röschel
MaRDI profile type: Publication
cites work: Q3956004
cites work: Q4477579
cites work: Kinematik der hpyerbolischen Ebene. I.
cites work: Q4023706
cites work: Generalization of the inflection circle to plane Euclidean kinematics on Cayley/Klein constraint motions of the first kind
full work available at URL: https://doi.org/10.1007/bf03322190
OpenAlex ID: W2073725833
description: scientific article; zbMATH DE number 933266