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Course, academic year 2019/2020
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Non-Euclidean Geometry II - NMUG402
Title in English: Neeukleidovská geometrie II
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2015
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: Mgr. Lukáš Krump, Ph.D.
Class: M Bc. DGZV
M Bc. DGZV > Povinné
M Bc. DGZV > 2. ročník
Classification: Mathematics > Geometry
Incompatibility : NDGE021
Interchangeability : NDGE021
Annotation -
Last update: T_KDM (04.05.2015)
Axiomatic of geometry, non-Euclidean geometries, models of non-Euclidean geometries (Beltrami-Klein, Poincare), groups of transformations.
Aim of the course -
Last update: T_KDM (04.05.2015)

This course helps to obtain theoretical background for teaching mathematics at high school.

Course completion requirements - Czech
Last update: Mgr. Lukáš Krump, Ph.D. (21.02.2018)

Zápočet se udílí za referát přednesený na cvičení, v opodstatněných důvodech (delší omluvená absence) lze zápočet alternativně získat za písemné zpracování referátu.

Povaha této kontroly studia vylučuje opakování této kontroly.

Zápočet je nutnou podmínkou účasti u zkoušky.

Literature -
Last update: T_KDM (04.05.2015)

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

Teaching methods -
Last update: T_KDM (04.05.2015)

Lectures and exercises.

Syllabus -
Last update: T_KDM (04.05.2015)

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.

 
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