Geometry

The axiomatic foundation for neutral, Euclidian and hyperbolic geometry is treated. Different models for hyperbolic geometry are discussed. Geometric constructions are treated. The course gives deep insight into topics in geometry that are central in school mathematics, and discusses the historical development of these topics.

1. Knowledge: The student has a basic understanding of the axiomatic approach to geometry, as well as of logical concepts and proof structures. The student is familiar with central theorems of neutral, Euclidean and hyperbolic geometry as well as the historical development of axiomatic geometry. The student has insight into geometric constructions and their relevance in a school teaching context..

2. Skills: The student is able to solve problems from elementary Euclidean and hyperbolic and neutral geometry, use models for axiomatic geometry and explain them to others. The student is able to justify geometric constructions made with straightedge and compass.

Lectures, exercises and written final examination. A certain number of problem sets must be approved in order to take the final exam. Physical or digital gatherings (agreed upon at the start of the semester with the students)