Sirli Markeyan: Hyperbolisk geometri

Abstract.

This study provides an overview of the concepts and history of hyperbolic geometry, a branch of mathematics distinct from the more familiar euclidean geometry. We delve into the mathematical concepts underlying hyperbolic spaces and analyze their axiomatic structure. The focus is on the replacement of the parallel postulate and the development of non-euclidean geometries by mathematicians such as Lobatjevskij and Bolyai. Various models for hyperbolic geometry are presented, with an emphasis on the upper half-plane and a brief overview of Poincaré’s unit disk. Additionally, we highlight the role of Möbius transformations and their contribution to the understanding of hyperbolic geometry.