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Vyučující
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Juklová Lenka, RNDr. Ph.D.
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Mikeš Josef, prof. RNDr. DrSc.
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Peška Patrik, RNDr. Ph.D.
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Obsah předmětu
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1. Affine transformations: definition and basic properties. Associated homomorphism. Determination theorem. Analytical expression. 2. Affine transformation group: affinity module, equi-affinity. Fixed points and directions. Homothetic affinities, translations, central dilations. 3. Basic affinities and their geometric meaning. Classification of plane affinities. 4. Isometries: definition and basic properties. Analytical representation. The group of isometries. Reflections in hyperplanes. 5. Classification of isometries in Euclidean spaces of dimension 1, 2, 3. 6. Similarities: definition and basic properties. Analytical form. Similarity group. Decomposition into isometry and dilation. Use in constructions. Centre of similarity in the plane. 7. Circular mappings: circular inversion in the Möbius plane. Mapping of circular curves. Use of inversion in construction tasks. 8. Transformations of the Euclidean plane in complex coordinates. Analytical form of affine / isometric / similarity transformation.
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Studijní aktivity a metody výuky
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Přednášení, Dialogická (diskuze, rozhovor, brainstorming)
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Výstupy z učení
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The aim of the course is to explain the foundations and classification of affine, congruent (isometric), similarity and circular transformations. Students will understand the structure of transformation groups in Euclidean geometry and will learn analytical representation of such mappings and their applications in solving geometric construction problems.
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Předpoklady
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nespecifikováno
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Hodnoticí metody a kritéria
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Ústní zkouška, Písemná zkouška
- active participation in tutorials - written test (up to 3 attempts allowed) - delivery of all homework assignments Final form of assessment: colloquium (combined form).
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Doporučená literatura
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Benz W. (2012). Affine Geometry and Euclidean Spaces.
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Berger, M. (2004). Geometry I, II. Universitext Springer.
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Needham T. (1997). Visual Complex Analysis.
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