University of West Bohemia
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for academic year 2024/2025
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Course: Synthetic Geometry

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Course title Synthetic Geometry
Course code KMA/SG
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 1
Semester Summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Bizzarri Michal, Doc. RNDr. Ph.D.
  • Výrut Radek, Mgr.
Course content
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.

Learning activities and teaching methods
Interactive lecture, Lecture supplemented with a discussion, E-learning, Discussion, Multimedia supported teaching, Task-based study method, Individual study, Students' self-study, Self-study of literature, Lecture, Lecture with visual aids, Practicum
  • Contact hours - 36 hours per semester
  • Preparation for an examination (30-60) - 40 hours per semester
  • Undergraduate study programme term essay (20-40) - 32 hours per semester
prerequisite
Knowledge
understand basic elementary geometry and trigonometry within the scope of the secondary school curriculum
understand the basic principles of matrix algebra and vector calculus
understand the basic principles of elementary calculus
Skills
apply the acquired procedures to elementary geometric problems at the secondary school level
calculate vectors, matrices and determinants and solve systems of linear and quadratic equations
use the calculus apparatus for basic problems
Competences
N/A
N/A
N/A
N/A
learning outcomes
Knowledge
understand in basic terms the development of geometric axiomatic systems
explain the logical proofs of geometric propositions, in particular by using the method of direct proof and proof by contradiction
understand the basic properties of identities, similarities, affinities and circular inverses
be familiar with the features of dynamic geometry software for the needs of construction and visualization of geometric objects
Skills
solve geometric problems using the synthetic method
perform proofs of elementary geometric propositions, in particular by using the method of direct proof and proof by contradiction
use the properties of congruences, similarities, affinities and circular inverses to solve geometric problems
construct and apply geometric models of simple real-world problems
use appropriate dynamic geometry software for the construction and visualisation of geometric objects
Competences
N/A
N/A
N/A
teaching methods
Knowledge
Lecture
Lecture supplemented with a discussion
Practicum
Multimedia supported teaching
Task-based study method
Self-study of literature
Individual study
Skills
Lecture
Lecture supplemented with a discussion
Practicum
Multimedia supported teaching
Task-based study method
Individual study
Competences
Lecture
Lecture supplemented with a discussion
Practicum
Multimedia supported teaching
Task-based study method
Self-study of literature
Individual study
assessment methods
Knowledge
Combined exam
Seminar work
Skills
Combined exam
Seminar work
Competences
Combined exam
Seminar work
Recommended literature
  • Boček, L., Šedivý, J. Grupy geometrických zobrazení. SPN Praha, 1980.
  • Lávička, M. Geometrie 1 : Základy geometrie v rovině. 1. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-861-7.
  • Martin, G. E. Geometric constructions : with 112 figures. [1st ed.]. New York [etc.] : Springer, 1998. ISBN 0-387-98276-0.
  • Polák, J. Přehled středoškolské matematiky.. Praha : Prometheus, 2008. ISBN 978-80-7196-356-1.
  • Polák, J. Středoškolská matematika v úlohách II.. Praha : Prometheus, 1999. ISBN 80-7196-166-3.
  • Sekanina, M. a kol. Geometrie. 1. díl..
  • Švrček, Jaroslav; Vanžura, Jiří. Geometrie trojúhelníka. 1. vyd. Praha : SNTL, 1988.
  • Vyšín, J. Geometria pre pedagogické fakulty. 2.diel. Bratislava : Slovenské pedagogické nakladateĺstvo, 1970.
  • Vyšín, J. Geometrie pro pedagogické fakulty. 1. díl.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Geography in Education (18) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (19) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Geography in Education (17) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Geography in Education (16) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (18) Category: Chemistry courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (19) Category: Physical education and sport 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (15) Category: Informatics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (19) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Biology in Education (17) Category: Biology courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Biology in Education (18) Category: Biology courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (17) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Biology in Education (15) Category: Biology courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Geography in Education (1) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physics in Education (19) Category: Physics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Geography in Education (15) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (17) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (19) Category: Chemistry courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): English Language in Education (19) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (19) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (18) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (16) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (18) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Music in Education (19) Category: Art and applied art 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (17) Category: Chemistry courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physics in Education (17) Category: Physics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (17) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physics in Education (15) Category: Physics courses 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Biology in Education (19) Category: Biology courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Geography in Education (19) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (18) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (18) Category: Physical education and sport 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (17) Category: Physical education and sport 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (16) Category: Chemistry courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Biology in Education (16) Category: Biology courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Physics in Education (16) Category: Physics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (16) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (14) Category: Chemistry courses 2 Recommended year of study:2, Recommended semester: Summer
University of West Bohemia, date of update: 26.07.2024 23:53. Data created for academic year 2024/2025