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Lecturer(s)
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Káňa Michal, doc. RNDr. Ph.D.
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Breitfelder Ondřej, Mgr.
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Course content
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Historical development of geometry. Axiomatic structure and theorems of plane Euclidean geometry. Geometric transformations of the plane - rigid motions, similarities, affinities, and inversion. Groups of geometric transformations. Euclidean constructions and Apollonius' problems. Fundamentals of coordinate geometry. An introduction to non-Euclidean geometries (hyperbolic and elliptic geometry). For modelling several geometric problems, interactive dynamic geometry software is used.
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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, E-learning, Discussion, Multimedia supported teaching, Task-based study method, Individual study, Students' self-study, Self-study of literature, Lecture, Lecture with visual aids, Practicum
- Contact hours
- 36 hours per semester
- Preparation for an examination (30-60)
- 40 hours per semester
- Undergraduate study programme term essay (20-40)
- 32 hours per semester
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| prerequisite |
|---|
| Knowledge |
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| understand basic elementary geometry and trigonometry within the scope of the secondary school curriculum |
| understand the basic principles of matrix algebra and vector calculus |
| understand the basic principles of elementary calculus |
| Skills |
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| apply the acquired procedures to elementary geometric problems at the secondary school level |
| calculate vectors, matrices and determinants and solve systems of linear and quadratic equations |
| use the calculus apparatus for basic problems |
| Competences |
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| N/A |
| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| understand in basic terms the development of geometric axiomatic systems |
| explain the logical proofs of geometric propositions, in particular by using the method of direct proof and proof by contradiction |
| understand the basic properties of identities, similarities, affinities and circular inverses |
| be familiar with the features of dynamic geometry software for the needs of construction and visualization of geometric objects |
| Skills |
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| solve geometric problems using the synthetic method |
| perform proofs of elementary geometric propositions, in particular by using the method of direct proof and proof by contradiction |
| use the properties of congruences, similarities, affinities and circular inverses to solve geometric problems |
| construct and apply geometric models of simple real-world problems |
| use appropriate dynamic geometry software for the construction and visualisation of geometric objects |
| Competences |
|---|
| N/A |
| N/A |
| N/A |
| teaching methods |
|---|
| Knowledge |
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| Lecture |
| Lecture supplemented with a discussion |
| Practicum |
| Multimedia supported teaching |
| Task-based study method |
| Self-study of literature |
| Individual study |
| Skills |
|---|
| Lecture |
| Lecture supplemented with a discussion |
| Practicum |
| Multimedia supported teaching |
| Task-based study method |
| Individual study |
| Competences |
|---|
| Lecture |
| Lecture supplemented with a discussion |
| Practicum |
| Multimedia supported teaching |
| Task-based study method |
| Self-study of literature |
| Individual study |
| assessment methods |
|---|
| Knowledge |
|---|
| Combined exam |
| Seminar work |
| Skills |
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| Combined exam |
| Seminar work |
| Competences |
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| Combined exam |
| Seminar work |
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Recommended literature
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Boček, L., Šedivý, J. Grupy geometrických zobrazení. SPN Praha, 1980.
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Jacques Hadamard. Lessons in Geometry, Vol. 1: Plane Geometry. 2008. ISBN 9780821843673.
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Lávička, M. Geometrie 1 : Základy geometrie v rovině. 1. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-861-7.
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Martin, G. E. Geometric constructions : with 112 figures. [1st ed.]. New York [etc.] : Springer, 1998. ISBN 0-387-98276-0.
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Polák, J. Přehled středoškolské matematiky.. Praha : Prometheus, 2008. ISBN 978-80-7196-356-1.
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Polák, J. Středoškolská matematika v úlohách II.. Praha : Prometheus, 1999. ISBN 80-7196-166-3.
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Sekanina, M. a kol. Geometrie. 1. díl..
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Švrček, Jaroslav; Vanžura, Jiří. Geometrie trojúhelníka. 1. vyd. Praha : SNTL, 1988.
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Vyšín, J. Geometria pre pedagogické fakulty. 2.diel. Bratislava : Slovenské pedagogické nakladateĺstvo, 1970.
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Vyšín, J. Geometrie pro pedagogické fakulty. 1. díl.
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