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Main menu for Browse IS/STAG
Course info
KMA / GVS
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Course description
Department/Unit / Abbreviation
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KMA
/
GVS
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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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Geometric View of the World
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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,
3
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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|
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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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0 / -
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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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71 / -
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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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Winter + Summer
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Semester taught
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Winter + Summer
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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 |
Yes
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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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This course focuses mainly on students with career paths other than mathematics or geometry. It introduces to students major ideas of geometry and its applications in the world around us. The main aim is to show how modern geometric methods contribute to studying and solving everyday problems of real life. The course also aims at giving the student a firm understanding of analytic method in Euclidean geometry, geometric transformations in the plane and in the space, fundamental theory of curves and surfaces including methods of their visualization using classical methods of descriptive geometry, as well as using 3D computer graphics software, and finally it enables the student to apply the methods in art, design, architecture, engineering, and on the role of geometry in education and our cultural heritage.
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Requirements on student
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During semester, students write two assignments (10 points each) - it is necessary to obtain at least 11 points from both. In addition, students have to write 2 homework assignments which will demonstrate knowledge of theory, constructions and applications.
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.
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Content
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Global and local coordinate systems. Fundamentals of plane and spatial analytic geometry. Polyhedra, polyhedral surfaces, Platonic and Archimedean solids, Golden ratio. Boolean operations, Feature Based Modelling. Descriptive geometry methods, Monge projection and linear perspective, non-linear projections, light and shadow. Geometric transformation in the plane and in the space. Curves and surfaces, their properties and visualization. Surfaces from special classes (rotational, translational, ruled, developable, helical, canal surfaces) and its application. Geometric methods application in art, design, architecture, engineering etc.
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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:
Pottmann, Helmut. Architectural geometry. 1st ed. Exton : Bentley Institute Press, 2007. ISBN 978-1-934493-04-5.
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Basic:
Meyer, Walter. Geometry and its applications. San Diego : Academic Press, 1999. ISBN 0-12-493270-3.
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Basic:
Černý, J., Kočandrlová, M. Konstruktivní geometrie. Česká technika ? nakladatelství ČVUT, 2004. ISBN 80-01-03089-X.
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Extending:
Urban, Alois. Deskriptivní geometrie. I.. Praha : SNTL, 1977.
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Extending:
Sekanina, M. a kol. Geometrie. 2. díl.. 1. vyd. Praha : Státní pedagogické nakladatelství, 1988.
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Recommended:
Urban, Alois. Deskriptivní geometrie. II.. Praha : SNTL, 1979.
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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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39
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Undergraduate study programme term essay (20-40)
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20
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Preparation for an examination (30-60)
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30
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Preparation for formative assessments (2-20)
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5
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Total
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94
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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 s ohledem na reálné funkce jedné a dvou prouměnných |
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 |
řešit vhodné soustavy polynomiálních 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: |
rozumět použití analytické metody v geometrii |
rozumět základním vlastnostem elementárních geometrických zobrazení v rovině a v prostoru |
orientovat se v popisu elementárních geometrických objektů (zejména speciálních tříd křivek a ploch) |
chápat vývoj geometrie jako součást našeho kulturního dědictví |
Skills - skills resulting from the course: |
aktivně používat analytickou metodu při řešení základních i aplikovaných úloh |
rozeznávat základní tvary ve světě kolem nás (mnohostěny, křivky, plochy, diskrétní povrchy, atd.) |
provádět vhodný rozklad složitějších geometrických objektů na základní prvky |
analyzovat vybrané geometrické vlastnosti, především s ohledem na jejich aplikační využití ve své studijní a budoucí profesní specializaci |
nalézat a využívat aplikační možnosti nejen v geometrii, ale i v přírodních vědách, počítačové grafice, průmyslovém designu atd. |
Competences - competences resulting from the course: |
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 |
Test |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Test |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
Test |
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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 |
Individual study |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Lecture supplemented with a discussion |
Practicum |
Multimedia supported teaching |
Individual study |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Lecture supplemented with a discussion |
Practicum |
Multimedia supported teaching |
Individual study |
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