Syllabus
Review of the historical development of geometry.
Geometry as a theoretical discipline, axiomatic building of geometry.
Axiomatic building of euclidean geometry: axioms, incidence, order, congruence, parallelism, continuity.
Lobachevski geometry: absolute geometry, Lobachevski axiom, historical notes to the fifth postulate, Beltrami-Klein model, etc.
Systems of axims and their properties, ways towards non-euclidean geometry.
Annotation
The course focuses on the axiomatic building of geometry (mathematical theory) and on the work with selected modesl of non-Euclidean geometries (hyperbolic, elliptic) with the goal to understand the geometric description of real world.