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Synthetic Geometry III - OKBM1M120A

Title:	Syntetická geometrie III
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2022
Semester:	winter
E-Credits:	4
Examination process:	winter s.:
Hours per week, examination:	winter s.:0/0, Ex [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
Teaching methods:	combined
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.
Pre-requisite :	OKBM1M102A

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: Mgr. Marie Holíková, Ph.D. (07.05.2018)

The subject extends Synthetic Geometry I and II. Historic and modern proofs of important synthetic geometry theorems are shown to students. Geometric problems from higher mathematical competitions are discussed.

Literature -

Last update: doc. RNDr. Antonín Jančařík, Ph.D. (29.10.2019)

KUŘINA, F. 10 pohledů na geometrii. Praha: Matematický ústav AV ČR, 1996, ISBN 80-85823-21-7
BOČEK, L., ZHOUF, J.: Planimetrie. Praha : PedF UK 2009. ISBN 978-80-7290-594-2
KUŘINA, F.: Umění vidět v matematice. Praha : SPN 1989. ISBN 80-04-23753-3
KUŘINA, F.: 10 geometrických transformací. Praha : Prometheus 2002. ISBN 80-7196-231-7

Requirements to the exam -

Last update: doc. RNDr. Antonín Jančařík, Ph.D. (29.10.2019)

A seminar paper on chosen topic, completing homework, test (two corrective tests in given terms).

Syllabus -

Last update: Mgr. Marie Holíková, Ph.D. (07.05.2018)

Different proofs of Pythagoras' theorem, Euclid's theorems and other important theorems.
A quadrilateral and its properties, quadrilaterals circumscribed and inscribed into a circle and their use in exercises.

A circle and its use in geometric problems.
Means (arithmetic, geometric, harmonic, quadratic) and their geometric interpretation.
Metric properties of planar and spatial objects.
Use of congruencies and similarities in planar and spatial geometric problems.
Regular and semiregular polyhedra.

Course completion requirements -

Last update: Mgr. Marie Holíková, Ph.D. (07.05.2018)

A seminar paper on chosen topic, completing homework, test (two corrective tests in given terms).