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Axiomatic of geometry, non-Euclidean geometries, models of non-Euclidean geometries
(Beltrami-Klein, Poincare), groups of transformations.
Last update: T_KDM (04.05.2015)
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This course helps to obtain theoretical background for teaching mathematics at high school.
Last update: T_KDM (04.05.2015)
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The course credit (="zápočet") is obtained for an oral essay; in well-reasoned cases (longer justified absence), the essay can be in a written form.
The nature of this study control excludes repeating.
The course credit is a necessary condition for admission to the exam. Last update: Krump Lukáš, Mgr., Ph.D. (29.10.2019)
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1. Kutuzov, B.V.: Lobačevského geometrie a elementy základů geometrie, ČSAV, Praha, 1953
2. Trajnin, J.L.: Osnovanija geometrii, Moskva, 1961
3. Hlavatý, V.: Úvod do neeuklidovské geometrie, JČMF, Praha, 1949
4. Čech, E.: Základy analytické geometrie II., Praha, 1952
5. Boček, L. & Šedivý J.: Grupy geometrických zobrazení, SPN, Praha
6. Weblen, O. & Young, J.W.: Projective geometry I.II., Blaisdell P. C., New York, 1938
7. Gans, D.: An Introduction to Non-Euclidean Geometry, Academic Press, New York, 1973
8. Tuller, A.: Introduction to Geometries,
9. Springer, C.E.: Geometry and Analysis of Projective Spaces,
10. Wolfe, H.E.: Introduction to Non-Euclidean Geometry, Holt, Rinehart & Winston, Inc., New York, 1966
Last update: T_KDM (04.05.2015)
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Lectures and exercises. Last update: T_KDM (04.05.2015)
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The exam is oral, its contents corresponds to the syllabus in the extent taught. Last update: Krump Lukáš, Mgr., Ph.D. (29.10.2019)
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Spherical geometry, excess of angles in spherical triangle, solution of spherical triangles.
Stereographic projection and circular inversion. Solutions of problems of Apollonios.
Axiomatisation of geometry, absolute geometry, the 5th postulate, mutual position of two lines in non-Euclidean geometry, defect of angles and area of triangle. Sheaves of lines and sets of corresponding points.
Models of non-Euclidean geometry. Distances and angles in the Poincare and Beltrami- Klein models. Riemannian metric and groups of transformations of models. Last update: T_KDM (04.05.2015)
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