Original scientific paper

Osculating Circles of Conics in Cayley-Klein Planes

Gunter Weiss ; Institute for Geometry, Technical University of Dresden, Dresden, Germany
Ana Sliepčević ; Faculty of Civil Engineering, University of Zagreb, Zagreb, Hrvatska

Abstract

In the Euclidean plane there are several well-known methods of constructing an osculating (Euclidean) circle to a conic. We show that at least one of these methods can be “translated” into a construction scheme of finding the osculating non-Euclidean circle to a given conic in a hyperbolic or elliptic plane. As an example we will deal with the
Klein-model of these non-Euclidean planes, as the projective geometric point of view is common to the Euclidean as well as to the non-Euclidean cases.

Keywords

Cayley-Klein plane; elation; pencil of conics; osculating circle; curvature centre

Hrčak ID:

47616

URI

https://hrcak.srce.hr/47616

Publication date:

25.1.2010.

Article data in other languages: croatian

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