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Geometry with Computer

Type of study Bachelor
Language of instruction Czech
Code 230-0442/01
Abbreviation GP
Course title Geometry with Computer
Credits 5
Coordinating department Department of Mathematics
Course coordinator Mgr. Dagmar Dlouhá, Ph.D.

Osnova předmětu

Program of lectures
=================

Week Lecture content
-------------------------------------------------- -----------------------------
1 Basic geometric objects (point, line, plane), concepts and constructions
2 Planimetry - properties of triangles, construction of basic triangles (height, center of gravity, angles)
3 Planimetry - construction of triangles advanced, uniformity (tangent of two circles, triangle inscribed in squares)
4 Conic sections - derivation from a rotational conical surface, definition and construction of an ellipse
5 Conics - definition and construction of a hyperbola
6 Conic sections - definition and construction of a dish
7 Kinematic geometry - elliptic and cardioid motion, conchoidal and cyclic movements
8 Stereometry - cube sections, slices of other bodies
9 Modeling and 3D Printing - Introduction to 3D Modeling and 3D Printing (Technology, Materials)
10 Modeling and 3D Printing - Basic Bodies (Spheres, Cylinders, Cones, Blocks)
11 Modeling and 3D Printing - Transform (Shift, Rotate, Scale)
12 Modeling and 3D Printing - Set Operations (Unification, Intersection, Difference)
13 Modeling and 3D Printing - Visual Programming (Mathematical Functions, Cycles)
14 Reserve



Exercise and seminar program + individual student work
================================================== ======

Week Content of seminars and seminars
-------------------------------------------------- -----------------------------
1 Basic geometric objects (point, line, plane), concepts and constructions
2 Planimetry - properties of triangles, construction of basic triangles (height, center of gravity, angles)
3 Planimetry - construction of triangles advanced, uniformity (tangent of two circles, triangle inscribed in squares)
4 Conic sections - derivation from a rotational conical surface, definition and construction of an ellipse
5 Conics - definition and construction of a hyperbola
6 Conic sections - definition and construction of a dish
7 Kinematic geometry - elliptic and cardioid motion, conchoidal and cyclic movements
8 Stereometry - cube sections, slices of other bodies
9 Modeling and 3D Printing - Introduction to 3D Modeling and 3D Printing (Technology, Materials)
10 Modeling and 3D Printing - Basic Bodies (Spheres, Cylinders, Cones, Blocks)
11 Modeling and 3D Printing - Transform (Shift, Rotate, Scale)
12 Modeling and 3D Printing - Set Operations (Unification, Intersection, Difference)
13 Modeling and 3D Printing - Visual Programming (Mathematical Functions, Cycles)
14 Reserve

E-learning

http://www.studopory.vsb.cz
http://mdg.vsb.cz
(in Czech language)

Povinná literatura

Černý, J.: Geometry. Praha: Vydavatelství ČVUT, 1996. ISBN 80-01-01535-1.
Vavříková, Eva: Descriptive Geometry, VŠB – TUO, Ostrava 2005.
Foley, J., van Dam, A., Feiner, S., Hughes, J.: Computer Graphics-Principles and Practise. 2nd ed., Addison-Wesley, Reading, Massachusetts, 1990.
Stillwell, J.: Geometry of surfaces. New York: Springer, 1992. ISBN 0-387-97743-0.

Doporučená literatura

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.


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