**S****p****ecific Objectives of course: **

To familiarize mathematics students with the axiomatic approach to geometry from a logical, historical, and pedagogical point of view and introduce them with the basic concepts of Affine Geometry, Affine spaces and Platonic Ployhedra.

**Course Outline:**

**V****ector spaces and affine geometry: **

Collinearity of three points, ratio AB/BC. Linear combinations and linear dependent set versus affine combinations and affine dependent sets. Classical theorems in affine geometry: Thales, Menelaus, Ceva, Desargues. Affine subspaces, affine maps. Dimension of a linear subspace and of an affine subspace.

**E****u****clidean geometry**:

Scalar product, Cauchy-Schwartz inequality: norm of a vector, distance between two points, angles between two non-zero vectors. Pythagoras theorem, parallelogram law, cosine and sine rules. Elementary geometric loci.

**O****rthogonal transformations: **

Isometries of plane (four types),

Isometries of space (six types). Orthogonal bases.

**P****latonic polyhedra**:

Euler theorem on finite planar graphs.

Classification of regular polyhedra in space. Isometries of regular polygons and regular polyhedra.