Geometry (KMD/E-GMT)

  • 6 credits
  • Lecturer: doc. PaedDr. Lilla Koreňová, PhD., Ing. Tomáš Barot, Ph.D.
  • Lessons (Lectures + Exercises + Seminars): 1 + 0 + 1
  • Semester: Winter / Summer
  • Language of instruction: English
  • Language of consultation: English
  • Level of qualification (Bc., Mgr.):Bc., Mgr. (M7503 Erasmus+)
  • Method of completion: Examination

Synopsis / description / annotation:

The aim of the course is to understand the geometrical problems in plane and in space within the Euclidean geometry. The first part of geometry is explanation of properties and construction rules of geometrical figures in plane (planimetrics) and in space (stereometry). Students will be acquainted with the mutual position of formations in the plane and in the space. The section rules and rules for conic section are explained. The second part of the course is an analytical description of geometric figures in plane and solids in space using algebraic description using the parametric and non-parametric equations. The parametric expression will be based on operation with vectors. Theoretical knowledge is demonstrated on practical examples and also in mathematical software used for purposes of geometry - GeoGebra and ParaView.

Content:

  1. Planimetrics - basic figures (point, line, plane, half-line, line segment, convex and non-convex figure, polygon)
  2. Geometrical transformations in plane (displacement, rotation, center symmetry, axis symmetry, uniformity)
  3. Position properties in planimetrics
  4. Construction problems in planimetrics
  5. Stereometry - basic solids (polyhedral and rotating solid)
  6. Position properties of solids in stereometry
  7. Construction problems based on sections
  8. Conic sections
  9. Introduction to vector calculus
  10. Analytical expression of figures and solids by parametric equations
  11. Analytical expression of figures and solids by non-parametric equations
  12. Solving geometrical problems using software

Literature:

  • BOWSER, E. Elements of Plane and Solid Geometry. Book on Demand, 2013.
  • CHRISTERSSON, M. MalinC's GeoGebra-book. Available from: http://www.malinc.se/math/
  • RUSCZYK, R. Introduction to Geometry. AoPS, 2008.

Updated: 06. 02. 2020