SubjectsSubjects(version: 978)
Course, academic year 2025/2026
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Geometry - NMTM505
Title: Geometrie
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: winter
E-Credits: 2
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Zbyněk Šír, Ph.D.
Mgr. Dalibor Šmíd, Ph.D.
Teacher(s): Mgr. Dalibor Šmíd, Ph.D.
Incompatibility : NMUM503
Interchangeability : NMUM503
Is incompatible with: NMUM503
Is interchangeable with: NMUM503
Annotation - Czech
Kurzovní přednáška z geometrie pro navazující magisterské učitelské studium (konstruovatelnost pravítkem a kružítkem, klasifikace geometrií). Propojení geometrických témat se školskou matematikou (hlubší pohled na skalární součin a na základy školské geometrie).
Last update: Robová Jarmila, doc. RNDr., CSc. (04.06.2020)
Literature -

Basic literature:

Dlab V., Bečvář J.: Od aritmetiky k abstraktní algebře. Serifa, Praha, 2016.

Greenberg M. J.: Euclidean and Non-Euclidean Geometries: Development and History. 4rd ed. W. H. Freeman, 2007.

Stillwell J.: The Four Pillars of Geometry. Springer, 2010.

Additional literature:

Tignol J.-P.: Galois' Theory of Algebraic Equations. World Scientific Publishing, Singapore, 2001.

Wolfe H. E.: Introduction to Non-Euclidean Geometry. Dover Publications; Reprint 2012.

Stanovský D.: Základy algebry. Matfyzpress, Praha, 2010.

Last update: Halas Zdeněk, Mgr., DiS., Ph.D. (04.06.2020)
Syllabus -

Constructability with a ruler and compass

Constructible points and numbers. Duplication of a cube, trisection of an angle, quadrature of a circle. Constructability of regular polygons.

Classification of geometries

Fundamentals of Euclidean geometry, absolute geometry, pangeometry. Non-Euclidean geometries and their models.

Klein's Erlangen program, classification of geometries.

Riemannian classification of geometries, connection with differential geometry, significance of scalar product in geometry and in school mathematics.

Last update: Halas Zdeněk, Mgr., DiS., Ph.D. (04.06.2020)
 
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