Course Unit Code | 230-0441/01 |
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Number of ECTS Credits Allocated | 5 ECTS credits |
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Type of Course Unit * | Compulsory |
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Level of Course Unit * | First Cycle |
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Year of Study * | Second Year |
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Semester when the Course Unit is delivered | Summer Semester |
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Mode of Delivery | Face-to-face |
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Language of Instruction | Czech |
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Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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Name of Lecturer(s) | Personal ID | Name |
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| DLO44 | Mgr. Dagmar Dlouhá, Ph.D. |
| VOL18 | RNDr. Jana Volná, Ph.D. |
Summary |
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Descriptive geometry is a practical discipline which tries to improve development of space and creative abalities and logical thinking. First it shows commonly used types of projection methods. At the socond part the geometric characteristics of relevant curves and surfaces folows. |
Learning Outcomes of the Course Unit |
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• to train development of space abilities
• to handle by different types of projection methods, to understand to their principles, to be familiar with their properties, advantages and disadvantages
• to acquaint with geometric characteristics of curves and surfaces that are used in technical practice of a given specialization
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Course Contents |
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1. Improper elements. Conics - basic concepts and focal properties.
2. Construction of ellipse, hyperbola and parabola from given elements.
3. The basic properties of projection. Parallel projection.
4. Central collineations and axial affinity in plane.
5. Projection with dimensions - view of point, line and plane.
6. Projection with dimensions - position tasks.
7. Projection with dimensions - metric problems.
8. Affine relationship between circle and ellipse. Projection of a circle in the projection with dimensions.
9. Orthogonal axonometry. Position tasks.
10. Metric problems and the projection of a circle in coordinate planes.
11. Elementary surfaces and solids. Basic concepts and properties.
12. Planar cut. Intersections with a line. Tangent plane.
13. Topographical surfaces.
14. Reserve. |
Recommended or Required Reading |
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Required Reading: |
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Vavříková,E.:Descriptive Geometry,VŠB – TU,Ostrava 2005, ISBN 80-248-1006-9.
http://mdg.vsb.cz/portal/dg/DeskriptivniGeometrie.pdf
Černý, J.: Geometry. Praha: Vydavatelství ČVUT, 1996. ISBN 80-01-01535-1.
Stillwell, J.: Geometry of surfaces. New York: Springer, 1992. ISBN 0-387-97743-0. |
Restl,Č.-Doležal,J.: Kótované promítání a topografické plochy, Ostrava, VŠB - TU 2004. ISBN 80-248-0651-7.
Urban,A.:Deskriptivní geometrie I,SNTL,Praha 1965.
http://mdg.vsb.cz/portal/dg/DeskriptivniGeometrie.pdf
Vavříková,E.:Descriptive Geometry, Ostrava, VŠB – TU 2005. ISBN 80-248-1006-9. |
Recommended Reading: |
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Kreyszig, E.: Differential geometry. New York: Dover Publications, 1991. ISBN 0-486-66721-9.
Kobayashi, S.: Transformation groups in differential geometry. Berlin: Springer, 1972. Classics in mathematics. ISBN 3-540-05848-6.
Umehara, M. and Yamada, K.: Differential geometry of curves and surfaces. Kaiteiban. Translate Rossman, W.. Singapore: World Scientific, 2017. ISBN 978-981-4740-23-4.
Falconer, K. J. Fractal geometry: mathematical foundations and applications. 3rd ed. Chichester: Wiley, 2014. ISBN 978-1-119-94239-9. |
Cholevová,I.- Lubojacký,B. - Restl,Č.: Sbírka řešených příkladů
z deskriptivní a konstruktivní geometrie, díl 2, Kótované promítání. Ostrava, VŠB-TU 1998. ISBN 80-7078-276-5.
Dudková,K. - Hamříková,R.: Kuželosečky, kolineace. Ostrava, VŠB-TU 2005. ISBN 80-248-0766-1.
Doležal,J. - Poláček,J.: Pravoúhlá axonometrie - sbírka řešených úloh. Ostrava, VŠB-TU 2013. ISBN 979-80-248-2989-0.
Černý, J.: Geometry. Praha: Vydavatelství ČVUT, 1996. ISBN 80-01-01535-1. |
Planned learning activities and teaching methods |
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Lectures, Individual consultations, Tutorials, Other activities |
Assesment methods and criteria |
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Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing |
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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 20 | 5 |
Examination | Examination | 80 (80) | 30 |
Písemná zkouška | Written examination | 60 | 25 |
Ústní zkouška | Oral examination | 20 | 5 |