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Course, academic year 2018/2019
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Projective geometry I - NMUG106
Title in English: Projektivní geometrie I
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2014 to 2018
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: Mgr. Lukáš Krump, Ph.D.
Class: M Bc. DGZV
M Bc. DGZV > Povinné
M Bc. DGZV > 1. ročník
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
Incompatibility : NDGE003
Interchangeability : NDGE003
Annotation -
Last update: T_KDM (20.04.2012)
Construction of projective plane and projective extension of Euclidean plane. Description of conics and construction of conics from given elements.
Aim of the course -
Last update: T_KDM (20.04.2012)

This course helps to obtain theoretical background for teaching mathematics at high school.

Course completion requirements - Czech
Last update: Mgr. Lukáš Krump, Ph.D. (21.02.2018)

Zápočet se udílí za aktivitu na cvičeních, v opodstatněných důvodech (delší omluvená absence) lze zápočet alternativně získat za vypracování zadaných domácích úkolů.

Povaha této kontroly studia vylučuje opakování této kontroly.

Zápočet je nutnou podmínkou účasti u zkoušky.

Literature -
Last update: T_KDM (20.04.2012)

Havlíček, K.: Úvod do projektivní geometrie kuželoseček. Praha, SNTL 1956

Bureš, J.- Burešová, J.: Projektivní geometrie I. Skripta MFF UK Praha

Kadleček, J.: Sto úloh z projektivní geometrie. Text KDM MFF UK, Praha 1995

Kadeřávek-Klíma-Kounovský: Deskriptivní geometrie I. Praha, od 1926

Kadleček: Základy geometrie. Skripta MFF UK Praha

Medek: Úvod do projektivnej geometrie. Bratislava, SPN 1975

Teaching methods -
Last update: T_KDM (20.04.2012)

Lectures and exercises.

Syllabus -
Last update: T_KDM (20.04.2012)

Projective plane. Projective extension of Euclidean plane. Pappus' theorem. Prionciple of duality. Projectivity between one-dimensional forms. Involution. Projective definition of conic. Pascal's and Brianchon's theorem. Pole and polar line and their use in constructions. Pencil and series of conics. Focal properties of conics. Construction of conics from given elements. Central collineation, image of a circle in central collineation.

 
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