Original scientific paper

Elementary Constructions for Conics in Hyperbolic and Elliptic Planes

Gunter Weiss ; University of Technology Vienna, Vienna, Austria

Abstract

In the Euclidean plane there are well-known constructions of points and tangents of e.g. an ellipse c based on the given axes of c, which make use of the Apollonius definition of c via its focal points or via two perspective anities (de la Hire's construction). Even there is no parallel relation neither in a hyperbolic plane nor in an elliptic plane it is still possible to modify many of the elementary geometric constructions for conics, such that they also hold for those (regular) non-Euclidean planes. Some of these modications just replace Euclidean straight lines by non-Euclidean circles. Furthermore we also study properties of Thales conics, which are generated by two pencils of (non-Euclidean) orthogonal lines.

Keywords

hyperbolic plane; elliptic plane; conic sections; de la Hire; Apollonius; Thales

Hrčak ID:

151332

URI

https://hrcak.srce.hr/151332

Publication date:

19.1.2016.

Article data in other languages: croatian

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