Articles
Charakteristische Dreieckpunkte in der projektiv-erweiterten hyperbolischen Ebene
Published:
2007-12-01
https://doi.org/10.5485/TMCS.2007.0142
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Keywords
Cayley-Klein model of the hyperbolic plane classification of H-triangles dual triangles characteristic points of the triangle
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Copyright (c) 2007 Ana Sliepčević and Ivanka Babić
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Ana, & Ivanka. (2007). Charakteristische Dreieckpunkte in der projektiv-erweiterten hyperbolischen Ebene. Teaching Mathematics and Computer Science, 5(2), 299-315. https://doi.org/10.5485/TMCS.2007.0142
Abstract
Some basic planimetric constructions regarding segments, angles and triangles are shown in the Cayley-Klein model of the hyperbolic plane. Relationship with the situation in the Euclidean plane is given. H-triangles are classified considering the location of their vertices and sides with respect to the absolute. There are 28 types of triangles. It is shown that there exist 12 pairs of dual triangles, while 4 types of triangles are dual to themselves. For every type of triangle the existence and number of the characteristic points are determined. Few examples of triangles with construction of their characteristic points, incircles and circumcircles are given.