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The students understand the geometrical terminology in the different types and appearances of geometry. They have the competence to experience with figures and shapes making use of computer software (geometry packages), even in case the dimension of the object is not restricted to the spatial world. Also knowledge of the applications of these, in history as well as in modern times. They demonstrate logically thinking and clear reasoning along the lines of ancient Greek mathematics. They have an overview of the correspondence between geometry and other disciplines within mathematics. Their final product is a report on a subject which has a link to geometry, or on a problem which can be approached by geometry. This product can be demonstrated in an animated presentation for a general audience and also for well informed people.
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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
- Perspective
- Group theory in relation to geometry
- Non-euclidean geometry
- Topology
- Spherical geometry
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