Course: Planimetry

« Back
Course title Planimetry
Course code KMA/PLA
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study 1
Semester Summer
Number of ECTS credits 3
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)
  • Pech Pavel, prof. RNDr. CSc.
  • Hašek Roman, Mgr. Ph.D.
Course content
1. Affine map. Affine transformation of a plane. 2. Plane congruences. Analytical expression. 3. Axial symmetry. 4. Revolution. Central symmetry. 5. Translation. 6. Glide reflection. 7. Composition of plane congruences. Direct and indirect congruences. Group of plane congruences. 8. Classification of congruences in E2. 9. Homothety. Composition of homotheties. 10. Homothety of circles. 11. Similarity. 12. Congruences and similarities in solving of construction tasks. 13. Axial affine map. 14. Summary

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming)
Learning outcomes
Affine map. Affine transformation of a plane. Plane congruences. Analytical expression. Axial symmetry. Revolution. Central symmetry. Translation. Glide reflection. Composition of plane congruences. Direct and indirect congruences. Group of plane congruences. Classification of congruences in E2. Homothety. Composition of homotheties. Homothety of circles. Similarity. Congruences and similarities in solving of construction tasks. Axial affine map.
A graduate will learn knowledge and skills corresponding to the affine maps of a plane and their use to solve problems within the range of the curriculum of the subject.
Prerequisites
Basics of Linear Algebra.

Assessment methods and criteria
Combined exam

Active participation on seminars. Written and oral examination of knowledge in the range of the course.
Recommended literature
  • Audin, M.:. Geometry, Springer, 2003.
  • Kuřina, F.:. Deset geometrických transformací, Prometheus, Praha, 2002.
  • Kuřina, F.:. 10 pohledů na geomatrii. Akademie věd České republiky, 1996.
  • Sekanina, M. a kol.:. Geometrie II, SPN, 1988.
  • Voráčová a kol.:. Atlas geometrie. Geometrie krásná a užitečná. Academia, Praha, 2012.
  • Vyšín, J. a kol.:. Geometrie pro pedagogické fakulty II, Bratislava, 1970.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Introductory teacher training course in mathematics (3) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Introductory teacher training course in mathematics (3) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer