Geometry can be build up in different ways. In an axiomatic way it was Euclides (300 BC) who introduced geometric figures that can be constructed by straightedge and compass. This is also our start of the course, but (linear) algebra smooths the later stages of geometry. The resulting analytical geometry gives us the generalisation of planar and solid geometry to higher dimensions. The origin of projective geometry lies in perspective paintings, Italian artists discovered in the 15th century how to draw three-dimensional scenes in correct perspective. All the different types of geometry can be defined by invariants of groups of transformations (Klein, 1872).
A list of different topics that will be dealt with:
- Euclid’s Elements
- Constructions with straightedge and compass
- Theorems ascribed to (famous) persons
- Vector geometry
- Group theory in relation to geometry
- Non-euclidean geometry
- Spherical geometry
Prerequisites : Linear Algebra (Math C1)
This course will take place in the first quartile of your second year. It will be taught by Gerard Jeurnink.
Gerard Jeurnink (1954) obtained his master degree in pure mathematics at Radboud University Nijmegen. Within the field of Functional Analysis he defended his PhD thesis ‘Integration of functions with values in a Banach lattice (1982, supervisor A. Van Rooij). Several years he practised geometrical phenomena in his math lessons at senior highschool, whereas during the last fifteen years he is the lecturer of the master course Geometry (University of Twente, Mastermath Utrecht). Besides his position at the department of Applied Mathematics he is also affiliated to the teacher training group ELAN. He organises refresher courses in Analytical Geometry. His main interest lies in the interaction between geometry and algebra.