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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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- Conics, focal properties of conics. - Axiomatic development of planimetry. Axioms of incidence, ordering, congruence, continuity and parallelism. - Geometric mapping on plane - concordance mapping, similar mapping. - Central collineation in plane. - Projection of conics by collineation. - Affinity in plane. - Projection of ellipse by affinity. - Set of points with property on plane. Power of a point with respect to a circle, chord. - Problem of Apollonius.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Demonstration of student skills, E-learning, Students' self-study
- Preparation for credit
- 28 hours per semester
- Preparation for exam
- 28 hours per semester
- Semestral paper
- 8 hours per semester
- Class attendance
- 56 hours per semester
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Learning outcomes
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Planimetry: conics, axiomatic geometry, congruent and similar mappings, affinity, power of a point with respect to a circle, radical axis.
Focal properties of conics. Geometric mapping in plane. Affinity and perspective collineation.
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Prerequisites
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Knowledge of secondary school mathematics.
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Assessment methods and criteria
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Oral exam, Written exam
Credit: Active participation on seminars. Work out the term's work. Submission of the homeworks. Knowledge of secondary school planimetry. Exam: test and interview
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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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Kouřim, J. a kol. Základy elementární geometrie pro učitelství l. st. ZŠ. Praha, SPN, 1985.
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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, SPN, 1991.
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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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