Journal for Geometry and Graphics 16 (2012), No. 1, 001--011
Copyright Heldermann Verlag 2012
On Kiepert Conics in the Hyperbolic Plane
Sybille Mick
Institute of Geometry, University of Technology, Kopernikusgasse 24, 8010 Graz, Austria
mick@tugraz.at
Johann Lang
Institute of Geometry, University of Technology, Kopernikusgasse 24, 8010 Graz, Austria
johann.lang@tugraz.at
The Kiepert hyperbola and the Kiepert parabola of a triangle in the Euclidean plane are the background of this paper. Its main issue is the question whether a similar phenomenon can be found in the hyperbolic plane. The considerations are set in the disk model of hyperbolic geometry where classical projective reasoning can also be employed.
Keywords: Elementary hyperbolic geometry, Cayley-Klein geometry, triangle geometry, Kiepert conics, hyperbolic isogonal transformation.
MSC: 51M09; 51N15, 51F99
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