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Lecturer(s)
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Mikeš Josef, prof. RNDr. DrSc.
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Peška Patrik, RNDr. Ph.D.
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Juklová Lenka, RNDr. Ph.D.
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Course content
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1. Afinne mappings: Definition and properties. Associated homomorfisms. The determination theorem. Analytic form. 2. Group of afinne transformations: Modul of affinity, equiafinity. Self-conjugate points and directions. Homothetic affinity translation and homothety. 3. Fundamental affinity and their meaning. Classification of affinity in planes. 4. Isometric mappings: Definition and properties. Analytic form. Group of izometry. Symmetry with respect to a hyperplain. 5. Classification of izometry on 1-, 2-, 3-dimensional Euclidian spaces. 6. Similarity mappings: Definition and properties. Analytic form. Group of similarity. Decomposition of similarity into isometry and homothety. Using similarity for solution of constructive problems and proofs. Construction of a center of similarity in a plane. 7. Potency of a point in a circle. Chordal of two circles. Bundle of circles. Apollonius and Papp's problems. 8. Cyclic mappings: Cyclic inversion in the Möbius plane. Mappings of cyclic curves. Using cyclic inversions for solution of constructive problems. 9. Transformation of Euclidean plain in complex coordinates. Analytic form of affine, isometric and similarity mappings.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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Describe principles and classification of affine mappings. Describe principles on differential geometry on curves, surfaces and manifold.
1. Knowledge Describe properties of affine mappings on affine spaces. Describe properties of the differential geometry of curves and surfaces and manifolds.
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Prerequisites
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Knowledge of affine and Euklidean spaces.
KAG/KGEI
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Assessment methods and criteria
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Oral exam, Written exam
Credit: the student has to participate actively in seminars and pass a written test.
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Recommended literature
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Berger, M. (1987). Geometry I, II. Universitext Springer-Verlag Berlin.
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Boček L. Sekanina M. (1988). Geometrie II. SPN Praha.
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Budinský B., Kepr B. (1970). Základy diferenciální geometrie s technickými aplikacemi. SNTL Praha.
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Doupovec, M. (1999). Diferenciální geometrie a tenzorový počet. VUT Brno.
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Jachanová, Marková, Žáková. (1989). Geometrie II. VUP Olomouc.
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