
05601305
j
2009e.00440
Sliep\v{c}evi\'{c}, Ana
Babi\'{c}, Ivanka
Characteristic triangle points in the projectiveextended hyperbolic plane. (Charakteristische Dreieckpunkte in der projektiverweiterten hyperbolischen Ebene.)
Teach. Math. Comput. Sci. 5, No. 2, 299315 (2007).
2007
,
DE
G45
G55
G95
CayleyKlein model of the hyperbolic plane
classification of Htriangles
dual triangles
characteristic points of the triangle
Summary: Some basic planimetric constructions regarding segments, angles and triangles are shown in the CayleyKlein model of the hyperbolic plane. Relationship with the situation in the Euclidean plane is given. Htriangles 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.