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Stereometry - NMTM205

Title:	Stereometrie
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:1/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Jarmila Robová, CSc. RNDr. Vlasta Moravcová, Ph.D.
Incompatibility :	NMUM205
Interchangeability :	NMUM205
Is incompatible with:	NMUM205
Is interchangeable with:	NMUM205

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: RNDr. Jakub Staněk, Ph.D. (12.06.2019)

The course is focused on the properties of geometric shapes and mapping in three-dimensional Euclidean space, deepens and extends the secondary school knowledge from stereometry. In particular, the synthetic approach is used to derive relationships, prove them, and in problem solving.

Course completion requirements -

Last update: doc. RNDr. Jarmila Robová, CSc. (14.10.2020)

The course is finalized by a credit from exercise class and by a final exam.

Requirements for receiving the credit from exercise class - distance learning:

1. Solution of tasks assigned in exercises (ZOOM). The tasks assigned and their solutions will be gradually published at https://www2.karlin.mff.cuni.cz/~robova/NMTM205-vystaveno/.

2. Successful completion of the credit test.

Requirements for receiving the credit from exercise class - full-time teaching:

1. Active attendance (including using drawing aids) - three absences are allowed. A higher number of absences can be replaced by the elaboration of seminar assignments.

2. Successful completion of the credit test.

Literature -

Last update: doc. RNDr. Jarmila Robová, CSc. (28.09.2020)

Secondary school Czech textbooks - Stereometry.

Kadleček, J.: Geometrie v rovině a v prostoru pro střední školy. Praha: Prometheus, 1996.

Kislev, A. P.: Kiselev's Geometry/Book II. Stereometry. El Cerrito, Calif.: Sumizdat, 2008.

Pomykalová, E.: Matematika pro gymnázia - stereometrie. Praha: Prometheus, 2008.

Kuřina, F.: Deset pohledů na geometrii. Praha: MÚ AV ČR, 1996.

Eukleides: Základy. Přeložil F. Servít, Praha: JČM, 1907.

Hejný, M.: Aj geometria naučila člověka myslieť. Bratislava: SPN, 1990.

Requirements to the exam -

Last update: doc. RNDr. Jarmila Robová, CSc. (14.10.2020)

The credit from exercise class is necessary for taking part in the final exam.

The oral exam has a form of colloquium. Requirements for the exam correspond to the syllabus of the subject to the extent that was presented at the lecture. In the case of distance lectures (ZOOM), the lecture materials will be gradually published at https://www2.karlin.mff.cuni.cz/~robova/NMTM205-vystaveno/.

Syllabus -

Last update: doc. RNDr. Jarmila Robová, CSc. (28.09.2020)

• Basic properties of geometric figures in three-dimensional space.

• Fundamental theorems of stereometry and their proofs.

• Positional and metric properties of spatial figures.

• Solids in oblique projection.

• Solids and their properties, particularly polyhedra, Euler's Theorem, Cavalieri's Principle.

• Geometric transformations in three-dimensional space (isometries, similarities).

• Geometric constructions in three-dimensional space.