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Lecturer(s)
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Vanžurová Alena, doc. RNDr. CSc.
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Jukl Marek, doc. RNDr. Ph.D.
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Course content
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1. Axiomatic principles of geometry. Incidence structure, incidence plane, examples. Parallelism in the incidence plane. 2. Affine planes axiomatically, homotheties. 3. Ordering axioms. 4. The Dedekind axiom of continuity. 5. Axioms of congruence. Consequences. 6. Absolute plane geometry. Existence of parallel lines. 7. The Archimedes axiom, the Cantor axiom, equivalent formulations. 8. Consequences of the fifth postulate. The Lobatchevski axiom, hyperbolic geometry, models (Beltrami-Klein, Poincaré).
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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Apply axiomatic method in geometry, compare first steps of Greek authors with modern approaches. Find common roots of Euclidean and hyperbolic geometry.
2. Comprehension Explain axiomatic method in geometry, differentiate between a modern approach and the approach of Euclid.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Systematic Observation of Student
Credit: the student should be present at least at 70% of classes, and participate actively. Colloquium: the student has to understand the subject.
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Recommended literature
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Cederberg N. (1995). A course in modern geometries. Springer Verlag.
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Kadleček J. (1974). Základy geometrie. SPN Praha.
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Kutuzov B. V. (1963). Lobačevského geometrie a elemnenty základů geometrie. ČSAV Praha.
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Millman R. S., Parker G. D. (1991). Geometry. A Metric Approach with Models. Springer.
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Sekanina M. (1988). Geometrie II. SNTL Praha.
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Vanžurová, A. (1986). Axiomatická výstavba geometrie. VUP Olomouc.
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