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Course, academic year 2019/2020
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Synthetic geometry II seminar - OB1310013
Title in English: Syntetická geometrie II prohlubující seminář
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2013
Semester: both
E-Credits: 2
Hours per week, examination: 0/2 C [hours/week]
Capacity: winter:unknown / unknown (200)
summer:unknown / unknown (200)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Level: basic
Is provided by: OKB1310N07
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
you can enroll for the course in winter and in summer semester
Guarantor: doc. RNDr. Naďa Vondrová, Ph.D.
Class: Matematika 1. cyklus - povinné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Co-requisite : OB2310202
Pre-requisite : OB2310012
Interchangeability : OKB2310013
Annotation -
Last update: JANCARIK/PEDF.CUNI.CZ (14.06.2010)
Basic notions and problems of 3D geometry are introduced. The course consolidates and deepens secondary school knowledge, while the cohesion of plane and 3D geometry is emphasized. The course helps the students understand the connection of geometry and real world more deeply.
Aim of the course -
Last update: JANCARIK/PEDF.CUNI.CZ (14.06.2010)

The goal is to introduce the basic notions and problems of 3D geometry. The course aims at systematization and development of secondary school knowledge.

Literature -
Last update: JANCARIK/PEDF.CUNI.CZ (14.06.2010)

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.: Stereometrie. Matematika pro gymnázia. Praha : Prometheus 2005.

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

Teaching methods -
Last update: JANCARIK/PEDF.CUNI.CZ (14.06.2010)

Lecture and seminars.

Syllabus -
Last update: JANCARIK/PEDF.CUNI.CZ (14.06.2010)

Affine properties of 3D figures. Mutual positions of lines and planes.

Metric properties of 3D figures.

Angle deviations of lines and planes, distances in space.

Sets of points of given properties.

Classification and composition of geometric congruences in space, group of congruences.

Basic properties of similarities in space. Classification and composition of similarities in space, group of similarities.

Polyhedra, Euler's theorem.

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