IMAp05 Geometry 1

Faculty of Education
Autumn 2022
Extent and Intensity
0/2/0. 3 credit(s). Type of Completion: k (colloquium).
Teacher(s)
Mgr. Leni Lvovská, Ph.D. (seminar tutor)
RNDr. Jakub Novák (seminar tutor)
Guaranteed by
Mgr. Leni Lvovská, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable of Seminar Groups
IMAp05/01: Wed 10:00–11:50 učebna 37, except Wed 26. 10., J. Novák
IMAp05/02: Wed 8:00–9:50 učebna 37, except Wed 26. 10., J. Novák
IMAp05/03: Tue 15:00–16:50 učebna 32, except Tue 25. 10., J. Novák
IMAp05/04: Tue 13:00–14:50 učebna 35, except Tue 25. 10., 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
Course objectives
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.
Syllabus
  • 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. Chosen geometrical exercises - proofs and constructions that are related to lecture Geometry 1 (YS1BP_PGE1). 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.
Literature
  • FRANCOVÁ, Marta and Leni LVOVSKÁ. Texty k základům ELEMENTÁRNÍ GEOMETRIE (Textbooks to the Basics of ELEMENTARY GEOMETRY). 1. vydání. Brno, 2014, 77 pp. ISBN 978-80-210-7594-8. info
  • FRANCOVÁ, Marta and Květoslava MATOUŠKOVÁ. Kapitoly ze základů stereometrie pro studium učitelství 1. stupně základní školy. Vyd. 1. Brno: Vydavatelství Masarykovy univerzity, 1994, 60 s. ISBN 8021008407. 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
  • 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
  • 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
Teaching methods
Lectures.
Assessment methods
Colloquium, discussion, written test.
Language of instruction
Czech
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 2018, Autumn 2019, autumn 2020, Autumn 2021, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2022, recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2022/IMAp05