Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Synthetic geometry I - OB2310N013

Title:	Syntetická geometrie I
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2019
Semester:	winter
E-Credits:	3
Examination process:	winter s.:
Hours per week, examination:	winter s.:2/1, C [HT]
Capacity:	unknown / unknown (999)
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Is provided by:	OPBM2M102A
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:	prof. RNDr. Naďa Vondrová, Ph.D.
Class:	Matematika 1. cyklus - povinné
Classification:	Mathematics > Mathematics General
Interchangeability :	OB2310012
Is pre-requisite for:	OB2310N016, OB2310N202, OB1310N007
Is interchangeable with:	OKB2310N13

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

Basic notions and problems of plane geometry are introduced. The course consolidates and deepens secondary school knowledge.

Aim of the course -

Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

The goal is to introduce the basic notions and problems of plane geometry. The course aims at systematization and development of secondary school knowledge. It helps the students understand the connection of geometry and real world more deeply.

Literature -

Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

Vyšín, J.: Geometrie pro pedagogické fakulty I,II. Praha, Bratislava : SPN 1965,1966.

Kuřina, F.: Umění vidět v matematice. Praha : SPN 1989.

Kuřina, F.: 10 geometrických transformací. Praha : Prometheus 2002.

Pomykalová, E.: Planimetrie. Matematika pro gymnázia. Praha : Prometheus 2005.

Sekanina, M. a kol.: Geometrie 1,2. Praha : SPN 1986.

Boček, L., Zhouf, J.: Planimetrie. Praha : PedF UK 2009.

Teaching methods -

Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

Lecture and seminars.

Requirements to the exam - Czech

Last update: Mgr. Michal Zamboj, Ph.D. (28.09.2017)

Podmínky k udělení zápočtu:
- aktivní účast na hodinách
- domácí řešení zadaných geometrických úloh
- napsání zápočtového testu - jsou 3 pokusy

Syllabus -

Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

Triangles. Quadrilaterals. Cyclic and tangential quadrilaterals. Circle. Circle power. Radical line. Euclidan constructions. Constructions using other tools. Sets of points of given properties. Definition and basic properties of geometric congruences in plane. Composition of geometric congruences. Classification of geometric congruences in plane. Direct and indirect geometric congruences. Group of geometric congruences. Definition and basic properties of homothecy. Similitude ration and its properties. Composition of homothecies. Monge's theorem. Circle in homothecy. Group of homothecies. Definition and basic properties of similarity. Decomposition of direct and indirect similarity (processes of construction). Similarity invariants (processes of construction). Classification of similarities in plane. Menelaos' and Ceva's theorem. Pappus's theorem. Double similitude ratio and its properties. Circle inversion (basic properties Apollonius' problems). Principles of axiomatic system conception of geometry.