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. Selfconjugate 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, 3dimensional 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/KGEO1 and KAG/KGEO2

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 SpringerVerlag Berlin.

Boček L. Sekanina M. (1988). Geometrie II. SPN Praha.

Jachanová, Marková, Žáková. (1989). Geometrie II. VUP Olomouc.
