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Course Information

M3722 Non-Euclidean geometry

Faculty of Science
Spring 2011

Extent and Intensity

2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).

Teacher(s)

Mgr. Vojtěch Žádník, Ph.D. (lecturer)

Supervisor

prof. RNDr. Josef Janyška, DSc.
Department of Mathematics and Statistics - Departments - Faculty of Science

Timetable

Mon 12:00–13:50 M6,01011

Prerequisites

Linear algebra and elementary projective geometry.

Course Enrollment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

Fields of study the course is directly associated with

• Mathematics (programme PřF, M-MA)
• Upper Secondary School Teacher Training in Descriptive Geometry (programme PřF, M-MA)
• Upper Secondary School Teacher Training in Descriptive Geometry (programme PřF, M-SS)
• Upper Secondary School Teacher Training in Mathematics (programme PřF, N-MA)
• Upper Secondary School Teacher Training in Mathematics (programme PřF, N-SS)

Course objectives

The aim of the course is to introduce the origins, basic notions, and models of non-Euclidean geometries.

Syllabus

• Classification of geometries, elementary Euclidean and neutral geometry.
• Introduction to hyperbolic geometry, angle of parallelism, spherical and hyperbolic trigonometry.
• Models of elliptic and hyperbolic plane, transformations in geometry.

Literature

• EUKLEIDES. Eukleidovy Základy : Elementa. Praha: Jednota českých matematiků a fysiků, 1907. 314 s. info
• GREENBERG, Marvin Jay. Euclidean and non-Euclidean geometries :development and history. 3rd ed. New York: W.H. Freeman, 1994. xvi, 483 s. ISBN 0-7167-2446-4. info
• KAGAN, V. F. Osnovanija geometrii : učenie ob obosnovanii geometrii v chode jego istoričeskogo razvitija. Čast' 1, Geometrija lobčevskogo i jeje predistorija. Moskva: Gosudarstvennoje izdatel'stvo techniko-teoretičeskoj literatury, 1949. 492 s. info
• COXETER, H. S. M. Introduction to geometry. 2nd ed. [New York]: John Wiley & Sons, 1989. xvi, 469 s. ISBN 0-471-50458-0. info
• Geometry. II, Spaces of constant curvature. Edited by E. B. Vinberg. Berlin: Springer-Verlag, 1993. 254 s. ISBN 3-540-52000-7-. info
• HLAVATÝ, Václav. Úvod do neeuklidovské geometrie. Vyd. 2. Praha: Jednota československých matematiků a fyziků, 1949. 227 s. info

Teaching methods

Lectures 2 hours a week, homeworks.

Assessment methods

Oral examination.

Further Comments

Study Materials
The course is taught once in two years.

Teacher's information

http://is.muni.cz/el/1431/jaro2011/M3722/op/index.html

The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2001, Spring 2002, Spring 2003, Spring 2005, Spring 2007, Spring 2009.

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