Original scientific paper

3rd Class Circular Curves in Quasi-Hyperbolic Plane Obtained by Projective Mapping

Helena Halas orcid.org/0000-0002-6890-7835 ; Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia
Ema Jurkin orcid.org/0000-0002-8658-5446 ; Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Zagreb, Croatia

Abstract

The metric in the quasi-hyperbolic plane is induced by an absolute figure F_{QH} = {F; f_1; f_2}, consisting of two real lines f_1 and f_2 incident with the real point F. A curve of class n is circular in the quasi-hyperbolic plane if it contains at least one absolute line.
The curves of the 3rd class can be obtained by projective mapping, i.e. obtained by projectively linked pencil of curves of the 2nd class and range of points. In this article we show that the circular curves of the 3rd class of all types, depending on their position to the absolute gure,
can be constructed with projective mapping.

Keywords

projectivity; circular curve of the 3rd class; quasi-hyperbolic plane

Hrčak ID:

174090

URI

https://hrcak.srce.hr/174090

Publication date:

16.1.2017.

Article data in other languages: croatian

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