| Area of Mathematics: | Algebra and Geometry (EAG) | ||
| Semester: | 5ο | ||
| Course ID: | 52204 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Ilias Tergiakidis | ||
Description
- The parallel postulate and its role in axiomatic foundation of geometry.
- Hilbert’s axioms. Continue axioms. Absolute Geometry.
- Klein’s view of Geometry. Geometric transformations. The Euclidean geometry of plane and space according to Klein’s viewpoint.
- Spherical geometry: Spherical distance. Orthogonal transformations. Euler’s theorem. Platonic solids.
- Hyperbolic geometry: Poincaré’s model. Distance function. Group of isometries. Areas.
Bibliography
- J.Greenberg Euclidean and Non-Euclidean Geometries, 4th Edition
- J. Ryan Euclidean and Non-Euclidean Geometry. An Analytic Approach
