Syllabus
Historic development of geometry.Axiomatic development of geometry, the absolute geometry. The parallel axiom and equivalent theorems.Axiom of incidence, ordering, conguence and continuity.
Lobachevsky's axiom and elementary properties of the hyperbolic geometry.Models of the planar hyperbolic geometry and their properties and mutual relations.Elemetary properties of the elliptic geometry.A sphere as a model of the elliptic geometry.
Annotation
The content of the subject is focused on the axiomatic development of geometry and selected models of non-euclidean geometries (hyperbolic, elliptic) with the aim to better understand geometrization of the real world.