Syllabus
Spherical geometry, excess of angles in spherical triangle, solution of spherical triangles.
Stereographic projection and circular inversion. Solutions of problems of Apollonios.
Axiomatisation of geometry, absolute geometry, the 5th postulate, mutual position of two lines in non-Euclidean geometry, defect of angles and area of triangle. Sheaves of lines and sets of corresponding points.
Models of non-Euclidean geometry. Distances and angles in the Poincare and Beltrami- Klein models. Riemannian metric and groups of transformations of models.
Annotation
Axiomatic of geometry, non-Euclidean geometries, models of non-Euclidean geometries
(Beltrami-Klein, Poincare), groups of transformations.