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Lecturer(s)
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Pirklová Petra, Mgr. Ph.D.
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Bímová Daniela, Mgr. Ph.D.
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Course content
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1. Axiomatic development of planimetry (systems of axioms of incidence, ordering, congruence, continuity and parallelism). 2. Elementary geometric objects in a plane. 3. Planimetric constructions of basic plane figures. 4. Constructions of the regular polygons. 5. Geometric mappings in the plane, congruent mappings in the plane. 6. Similar mappings in the plane. 7. Sets of all the points with the given properties, power of a point to a circle, chordal, potential point. 8. Conics, focal properties of conics. 9. Axis affinity in the plane. 10. Central collineation in the plane. 11. Representation of conics using planar axial affinity. 12. Representation of conics using planar central collineation. 13. Apollonius's problems. 14. Reserve.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments), Practicum, E-learning, Students' portfolio
- Class attendance
- 56 hours per semester
- Preparation for credit
- 28 hours per semester
- Preparation for exam
- 28 hours per semester
- Semestral paper
- 8 hours per semester
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Learning outcomes
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Planimetry. Repetition of basic planimetric terms, properties of geometric planar objects, congruent and similar mappings in the plane. Planimetric constructive problems. Enhancement of secondary school knowledge of students in the topic of conics, familiarization of students with topics as axial affinity and perspective collineation in the plane, a power of a point with respect to a circle, radical axis and potential point, Apollonius's problems.
Knowledge of basic planar structures and their properties, constructions of regular polygons, geometric mappings in the plane (congruent and similar mappings, axial affinity and perspective collineation), focal properties of the conics, and Apollonius's problems.
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Prerequisites
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Knowledge of secondary school mathematics and planimetry. Drawing skills.
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Assessment methods and criteria
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Oral exam, Written exam
Credit requirements: - active participation in exercises - successful submission of the planimetric construction task in written form - presentation of the given topic from planar geometry - presentation of sample solutions of at least two examples to practice the discussed topics
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Recommended literature
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Fabiánová, H. - Ocmanová, B. Opakování geometrie. Liberec, TUL, 1999. ISBN 80-7083-355-6.
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Kuřina, F. Deset geometrických transformací. Praha, Prometheus, 2002.
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Kuřina, F. Deset pohledů na geometrii. Praha, MÚ AV ČR, 1996.
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Polák, J. Přehled středoškolské matematiky. Praha, Prometheus, 2016. ISBN 978-80-7196-458-2.
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Přívratská, J. - Pecina, V. Kuželosečky. Liberec, TUL, 2004. ISBN 80-7093-855-8.
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Přívratská, J.:. Planimetrie (opakování). Liberec, TUL, 2002. ISBN 80-7083-650-4.
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Urban, A.:. Deskriptivní geometrie I, II. Praha, SNTL, 1967.
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