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Main menu for Browse IS/STAG
Course info
KMA / SG
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Course description
Department/Unit / Abbreviation
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KMA
/
SG
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Synthetic Geometry
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
4
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
2
[Hours/Week]
Tutorial
1
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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-
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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50 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Summer semester
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Semester taught
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Summer semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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-
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The aim of this course is to give students a thorough introduction to classical Euclidean geometry in the plane and active understanding of the fundamental concepts of elementary geometry such as:
- Euclid's Elements and axiomatic systems, Hilbert's axioms,
- Proving theorems of Euclidean Geometry,
- Polygons and Circles and their properties,
- Euclidean Constructions and Apollonius' problems,
- Geometric transformations and their applications,
- Basic concepts of non-Euclidean geometry.
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Requirements on student
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During semester, students have to write 4 homework assignments which will demonstrate knowledge of theory, constructions, applications, and proofs.
The final examination is in the form of a written exam (70% of the grade) which is supplemented by an oral examination (30% of the grade). All assessment tasks will assess the learning outcomes, especially, the ability to provide logical and coherent proofs of theoretical results and to analyze and solve specific problems related to Euclidean geometry in the plane.
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Content
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Historical development of geometry. Axiomatic structure and theorems of plane Euclidean geometry. Geometric transformations of the plane - rigid motions, similarities, affinities, and inversion. Groups of geometric transformations. Euclidean constructions and Apollonius' problems. Fundamentals of coordinate geometry. An introduction to non-Euclidean geometries (hyperbolic and elliptic geometry). For modelling several geometric problems, interactive dynamic geometry software is used.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Basic:
Vyšín, J. Geometria pre pedagogické fakulty. 2.diel. Bratislava : Slovenské pedagogické nakladateĺstvo, 1970.
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Basic:
Vyšín, J. Geometrie pro pedagogické fakulty. 1. díl.
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Basic:
Lávička, M. Geometrie 1 : Základy geometrie v rovině. 1. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-861-7.
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Extending:
Martin, G. E. Geometric constructions : with 112 figures. [1st ed.]. New York [etc.] : Springer, 1998. ISBN 0-387-98276-0.
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Extending:
Sekanina, M. a kol. Geometrie. 1. díl..
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Extending:
Boček, L., Šedivý, J. Grupy geometrických zobrazení. SPN Praha, 1980.
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Recommended:
Švrček, Jaroslav; Vanžura, Jiří. Geometrie trojúhelníka. 1. vyd. Praha : SNTL, 1988.
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Recommended:
Polák, J. Přehled středoškolské matematiky.. Praha : Prometheus, 2008. ISBN 978-80-7196-356-1.
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Recommended:
Polák, J. Středoškolská matematika v úlohách II.. Praha : Prometheus, 1999. ISBN 80-7196-166-3.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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36
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Undergraduate study programme term essay (20-40)
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32
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Preparation for an examination (30-60)
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40
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Total
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108
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
rozumět základním poučkám z elementární geometrie a trigonometrie v rozsahu učiva střední školy |
rozumět základním principům z maticové algebry a vektorového počtu |
rozumět základním principům elementárního kalkulu |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
aplikovat osvojené postupy na elementární geometrické úlohy na úrovni střední školy |
počítat s vektory, maticemi a determinanty a řešit soustavy lineárních a kvadratických rovnic |
používat aparát kalkulu na základní úlohy |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
chápat v základních rysech vývoj geometrických axiomatických systémů |
vysvětlovat logické důkazy geometrických tvrzení, obzvláště užitím metody přímého dokazování a důkazu sporem |
rozumět základním vlastnostem shodností, podobností, afinit a kruhové inverze |
orientovat se ve vlastnostech SW dynamické geometrie pro potřeby provádění konstrukcí a vizualizaci geometrických objektů |
Skills - skills resulting from the course: |
řešit geometrické úlohy syntetickou metodou |
provádět důkazy elementárních geometrických tvrzení, obzvláště užitím metody přímého dokazování a důkazu sporem |
využívat vlastnosti shodností, podobností, afinit a kruhové inverze při řešení geometrických úloh |
sestavovat a aplikovat geometrické modely jednoduchých reálných problémů |
používat vhodný software dynamické geometrie pro provádění konstrukcí a vizualizaci geometrických objektů |
Competences - competences resulting from the course: |
N/A |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Lecture supplemented with a discussion |
Practicum |
Multimedia supported teaching |
Task-based study method |
Self-study of literature |
Individual study |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Lecture supplemented with a discussion |
Practicum |
Multimedia supported teaching |
Task-based study method |
Individual study |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Lecture supplemented with a discussion |
Practicum |
Multimedia supported teaching |
Task-based study method |
Self-study of literature |
Individual study |
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