Rudiments of Geometry 360-MS1-2GELa
Ćwiczenia (CW) Rok akademicki 2022/23

Knows basic techniques of the analytical affine geometry; in particular: he can determine equations of a line, a plane, and of an arbitrary subspace characterized in terms of their geometrical position, can solve problems where the affine cross ratio is involved, can apply the Ceva and the Menelaos Theorem - tests, hoomeworks.

Knows fundamental types of affine transformations and their analytical characterization, can characterize affine transformations determined by means of simple invariants - tests, hoomeworks.

Knows fundamental systems of notions used to characterize Euclidean Geometry (orthogonality, equidistance); can characterize mutual position of spheres and subspaces. Can use inversion to translate problems of inversive (Moebius) geoemetry into the language of Euclidean Geometry and vice versa - tests, hoomeworks.

Knows and can use (in simple cases) principles of classification of isometries of Euclidean Spaces - tests, hoomeworks.

After completing the course student gets backgrounds enabling him to learn and develop classical geometry - solving tasks on a blackboard.

Analytical, coordinate affine space. Partition ratio of a segment. Barycentric coordinate system. The Ceva and the Menelaos theorem. Dilatations and affine maps.

Metric affine space. Symmetries, homotheties, isometries.