IMA05 Geometry 1

Faculty of Education
Autumn 2026
Extent and Intensity
0/2/0. 3 credit(s). Type of Completion: k (colloquium).
In-person direct teaching
Teacher(s)
doc. RNDr. Jaroslav Beránek, CSc. (seminar tutor)
Mgr. Petr Liczman (seminar tutor)
RNDr. Jakub Novák, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Jakub Novák, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable of Seminar Groups
IMA05/Kombi01: Fri 2. 10. 12:00–14:50 D32 učebna, Fri 16. 10. 15:00–17:50 D214 učebna, Fri 11. 12. 13:00–14:50 D32 učebna, J. Novák
IMA05/PrezSem01: Mon 10:00–11:50 D32 učebna, P. Liczman
IMA05/PrezSem02: Mon 12:00–13:50 D32 učebna, P. Liczman
IMA05/PrezSem03: Tue 16:00–17:50 D32 učebna, J. Novák
IMA05/Erasmus: No timetable has been entered into IS. J. Novák
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Abstract
At the end of the course students should be able to understand and explain the followed knowledge: Hilbertś system of axioms - concept of axioms, elementary terms derived from axioms of incidence, order, parallels, congruence and continuity. Elementary geometric shapes - triangles, quadrilaterals, circles and their properties. Foundations of theory of measure - length of line segments, measurement of angles, planar and spatial objects, principle of Jordanś measure. At the end of the course students should be able to solved chosen geometrical exercises. Weither at the end of the course students should be able to understand and explain the followed knowledge: Basic geometry terms, properties and relations between them, mainly terms included in subject matter of elementary school. Geometrical objects as a set of points. Solution of chosen proof exercises (mostly triangles, quadrangles and circles). Constructional and planimetric exercises and their solution.
Learning outcomes
At the end of the course students should be able to solved chosen geometrical exercises. Weither at the end of the course students should be able to understand and explain the followed knowledge: Basic geometry terms, properties and relations between them, mainly terms included in subject matter of elementary school. Geometrical objects as a set of points. Solution of chosen proof exercises (mostly triangles, quadrangles and circles). Constructional and planimetric exercises and their solution.
Key topics
Elementary geometric objects and theier properties:elementary notions and postulates of Euclidean geometry, elementary geometric figures (line segment, half line, half plane, half space, angle, triangle,quadrilateral, circle, broken line, polygon, polyhedron),convex and nonconvex sets of points, congruence of line segments and angles, consequential concepts. Spherical neighbourhoods in plane and space and derived notions. Elementary sets of points with certain property (geometrical locus). Rudiments of theory of measure: measurement of line segment, measurement of angle, measurement of planar and spatial objects - principle of Jordanś theory of measure. Solution of exercises.
Study resources and literature
    required literature
  • LVOVSKÁ, Leni and Jakub NOVÁK. Sbírka úloh z elementární geometrie pro studium učitelství 1. stupně základní školy (A collection of exercises in elementary geometry for students of primary school teaching). 1st ed. Masarykova univerzita, 2024, 59 pp. ISBN 978-80-280-0549-8. info
    not specified
  • FRANCOVÁ, Marta; Květoslava MATOUŠKOVÁ and Milena VAŇUROVÁ. Sbírka úloh z elementární geometrie. Vyd. 1. Brno: Masarykova univerzita v Brně, 1992, 86 s. ISBN 8021004045. info
  • FRANCOVÁ, Marta; Květoslava MATOUŠKOVÁ and Milena VAŇUROVÁ. Texty k základům elementární geometrie : pro studium učitelství 1. stupně základní školy. 2. opr. vyd. Brno: Masarykova univerzita, 1994, 107 s. ISBN 8021008806. info
  • KOUŘIM, Jaroslav; Ondrej ŠEDIVÝ and František KUŘINA. Základy elementární geometrie : pro učitelství 1. stupně ZŠ. 1. vyd. Praha: Státní pedagogické nakladatelství, 1985, 156 s. info
Approaches, practices, and methods used in teaching
Problem solving, short lectures.
Method of verifying learning outcomes and course completion requirements
Colloquium, discussion, written test.
Alternate completion (in Czech)
V případě zahraničního výjezdu je možné předmět absolvovat v náhradní podobě. Studující, kteří na výjezd odjíždí, se přihlásí do speciální seminární skupiny s příznakem Erasmus. Po návratu z výjezdu je nutné odevzdat vypracované úkoly dle interaktivní osnovy a zúčastnit se kolokvia. Úkoly musí být odevzdány nejméně jeden týden před plánovaným termínem kolokvia.
Language of instruction
Czech
Teacher's information
Studenti si mohou zaregistrovat navazující volitelný předmět Matematika 5. V rámci jeho výuky bude na základě dotazů studentů doplňován výklad témat zařazených do přednášek a seminářů z gemetrie a budou řešeny další úlohy, které musí studenti zvládnout.
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2025.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2026/IMA05