Charakteristische Dreieckpunkte in der projektiv-erweiterten hyperbolischen Ebene (CROSBI ID 125764)
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Sliepčević, Ana ; Babić, Ivanka
njemački
Charakteristische Dreieckpunkte in der projektiv-erweiterten hyperbolischen Ebene
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.
Cayly-Kleinsche Modell; hyperbolische Ebene; duale Dreieck; characteristische Dreieckpunkte;
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engleski
Characteristic Points of the Triangle in the hyperbolic Plane
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Cayley-Klein model of the hyperbolic plane; classification of H-triangles; dual triangles; characteristic points of the triangle
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