Triangles in spherical hyperbolic and de-sitter planes

This thesis consists of six chapters. In first and second chapter, historical information and fundamental concepts are given in Euclidian and hyperbolical spaces, respectively. The conformal triangles and their areas are obtained in chapter three, whereas new results are acquired through applying the technique of [4] to spherical and hyperbolical triangles in spherical and hyperbolical planes in fourth and fifth chapters, respectively. The existence of the spherical and hyperbolical conformal triangles is first shown in this study, respectively in fourth and fifth chapters. Furthermore, special spherical and hyperbolical triangles are issued in these chapters. In chapter six, triangle kinds in de-Sitter plane are examined and the area formulas are firstly obtained in this thesis for non-degenerate ones.