Course: Geometry 3

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Course title Geometry 3
Course code KAG/MGEO5
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Mikeš Josef, prof. RNDr. DrSc.
  • Juklová Lenka, RNDr. Ph.D.
Course content
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.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
Learning outcomes
Describe principles and classification of affine mappings.
1. Knowledge Describe properties of affine mappings on affine spaces.
Prerequisites
Knowledge of affine and Euklidean spaces.
KAG/MGEO3 and KAG/MGEO4

Assessment methods and criteria
Oral exam, Written exam

Credit: the student has to participate actively in seminars and pass a written test.
Recommended literature
  • Berger, M. (1987). Geometry I, II. Universitext Springer-Verlag Berlin.
  • Boček L. Sekanina M. (1988). Geometrie II. SPN Praha.
  • Jachanová, Marková, Žáková. (1989). Geometrie II. VUP Olomouc.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Mathematics (1) Mathematics courses 3 Winter