Skip to main content
Skip header

Descriptive Geometry

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code230-0441/01
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
DLO44Mgr. Dagmar Dlouhá, Ph.D.
VOL18RNDr. Jana Volná, Ph.D.
Summary
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
• 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
Course Contents
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
Required Reading:
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:
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
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit20 5
        ExaminationExamination80 (80)30
                Písemná zkouškaWritten examination60 25
                Ústní zkouškaOral examination20 5