Synthetic geometry I - OKBM1M102A
Title: Syntetická geometrie I
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2022
Semester: winter
E-Credits: 3
Examination process: winter s.:
Hours per week, examination: winter s.:0/0, C [HT]
Extent per academic year: 12 [hours]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: combined
Is provided by: OKBM3M012A
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: Mgr. Marie Holíková, Ph.D.
Is pre-requisite for: OKBM1M109A, OKBM1M125A, OKBM1M123A, OKBM1M120A
Opinion survey results   Examination dates   Schedule   Noticeboard   
Annotation -
The students will be with the use of synthetic approach introduced to the development and methods of solving constructive geometric tasks, geometric transformations in a plane, properties of planar shapes, and proofs of elementary theorems. The content's structure is focused on the consecutive systematic description of fundamental terms and orientation in geometry.
Last update: Zamboj Michal, Mgr., Ph.D. (13.09.2021)
Aim of the course -

The student will be able to use methods of synthetic geometry, solve planar geometric tasks, and learn theoretical principles necessary for a mathematics teacher and also for further studies. 

Last update: Zamboj Michal, Mgr., Ph.D. (20.09.2024)
Descriptors -

The materials are located in the LMS Moodle course Planimetrie (https://dl1.cuni.cz/course/view.php?id=7763) and on the webpage https://www2.karlin.mff.cuni.cz/~zamboj/SG1.html.

Students' tasks will be available in the LMS Moodle. 

The course will be carried out online in the case of suspension of in-person meetings. The link for online meetings will be available in the LMS Moodle.

Last update: Zamboj Michal, Mgr., Ph.D. (13.09.2021)
Course completion requirements -

Full-time form

Requirements for the exam (in-person form):

  • active participation (at least 80%)
  • attaining at least 60 points from the sum (max 100 points) for: minitests each week (starting from the 2nd week), half test, final test. There is no corrective date for individual tests. In the case of an insufficient amount of points, the summary test for both - half and final tests, will be carried out. 

In the case of suspended in-person teaching:

  1. the distant form of teaching will be strengthened by additional tasks and testing in the LMS Moodle 
  2. online meetings will be organized. Active participation using a camera and microphone on the students' side will be required. 

 

Combined form

Requirements for the exam:

  • active participation on teaching blocks
  • fulfilling tasks in the LMS Moodle
  • attaining at least 60 % of points for the final exam (1 proper and 2 corrective attempts)

In the case of suspended in-person teaching:

  • online meetings will be organized. Active participation using a camera and microphone on the students' side will be required. 
Last update: Zamboj Michal, Mgr., Ph.D. (13.09.2021)
Literature -

BOČEK, L., ZHOUF, J. Planimetrie. Praha, PedF UK, 2009.
KUŘINA, F. 10 geometrických transformací. Praha, Prometheus, 2002.
VYŠÍN, J. a kol. Geometrie pro pedagogické fakulty I, Státní pedagogické nakladatelství, 1965.
POMYKALOVÁ, E. Planimetrie. Matematika pro gymnázia. Praha, Prometheus, 2005.
MORAVCOVÁ, Vlasta a HROMADOVÁ, Jana. Základy planimetrie: pro učitelské studium. Praha: MatfyzPress, 2021. ISBN 978-80-7378-456-0.
LEISCHNER, P. Metody řešení planimetrických úloh, Jihočeská univerzita v Českých Budějovicích, Pedagogická fakulta, 2012.
LÁVIČKA, M. Syntetická Geometrie, Plzeň, ZČU, 2007.
GLAESER, G., STACHEL, H., ODEHNAL, B. The Universe of Conics. Springer, 2016.
COXETER, H.S.M. Introduction to geometry. Wiley, 2nd ed., 1989.

Last update: Zamboj Michal, Mgr., Ph.D. (10.09.2024)
Syllabus -
  • Structure and classification of constructive geometric tasks 
  • Collinear transformation, incidence, cross-ratio, Pappus' theorem, Desargues's theorem
  • Affine transformation, parallelism, affine ratio, Menelaus' and Ceva's theorem
  • Similarity transformation, angle, trigonometry
  • Isometric transformation, distance, area, classification of isometries, theorems on triangles
  • Circle and its properties
  • Polygons
  • Loci given by certain conditions, conics
  • Circle inversion
  • Apollonius' problems
Last update: Zamboj Michal, Mgr., Ph.D. (13.09.2021)
Learning resources -
https://dl1.cuni.cz/course/view.php?id=7763
Last update: Zamboj Michal, Mgr., Ph.D. (13.09.2021)
Learning outcomes - Czech
  • Studující vyřeší konstrukční úlohy různých typů.
  • Studující řeší úlohy syntetické geometrie různými metodami.
  • Studující zobrazuje útvary pomocí geometrických zobrazení v rovině (kolineární, afinní, podobné, shodné, kruhová inverze) a analyzuje jejich vlastnosti.
  • Studující formuluje definice elementárních geometrických útvarů.
  • Studující formuluje a dokazuje elementární geometrické věty.
  • Studující konstruuje a určuje množiny body daných vlastností.
Last update: Zamboj Michal, Mgr., Ph.D. (20.09.2024)