Professional paper

Some collineations of H-plane

Ivanka Babić ; Polytechnic Zagreb, Zagreb, Croatia

Abstract

On the Klein's model of the hyperbolic plane the harmonic homology is defined. This collineation maps absolute points of the h-plane onto absolute points, real points onto real points and ideal points onto ideal points. It is called line symmetry if the center of collineation is ideal point and point symmetry if the center is real point, because described mappings have equal properties as the analogues mappings in the Euclidean plane. By using point and line symmetries, symmetric images of the lines, points and triangles, bisectors of the angles and perpendicular bisectors of the segments are constructed. At the end one complicated metric problem is solved.

Keywords

hyperbolic plane; Klein's model of the hyperbolic plane; central involutory collineation

Hrčak ID:

3328

URI

https://hrcak.srce.hr/3328

Publication date:

15.2.2006.

Article data in other languages: croatian

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