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Lecturer(s)
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Bímová Daniela, Mgr. Ph.D.
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Pirklová Petra, RNDr. Ph.D.
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Course content
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Course programme : 1. Principles of Monge projections. Projection of points, straight lines, planes. 2. Point of intersection of a straight line and a plane, parallel and intersecting planes. (Plane section of prisms and pyramids.) 3. Straight line perpendicular to a plane, distance of linear objects. Rotation of a plane into a projection plane. 4. Orthogonal projection of a circle. Elementary solids in general position, contour lines visibility. 5. Analytic geometry v E3. Vectors, coordinates of vectors and points. Parametric equation of a straight line and a plane. 6. General equation of a plane. Position and metric problems in E3. 7. Vector function of one real variable. Definition and equation of a curve, tangent. 8. Accompanying trihedron , flection and torsion. 9. Helix. Equation, basic properties. Constructive problems. 10. Surface, curves on a surface, tangent plane. Surface of revolution (sr), meridian, tangent plane. 11. Constructive problems, plane section, intersection. 12. Helicoids. Definition, basic properties and constructive problems. 13. Cyclic helicoids. Ruled helicoids. 14. Reserve. Practice 1. Principles of Monge projections. Projection of points, straight lines, planes. 2. Point of intersection of a straight line and a plane, parallel and intersecting planes. (Plane section of prisms and pyramids.) 3. Straight line perpendicular to a plane, distance of linear objects. Rotation of a plane into a projection plane. 4. Orthogonal projection of a circle. Elementary solids in general position, contour lines visibility. 5. Analytic geometry v E3. Vectors, coordinates of vectors and points. Parametric equation of a straight line and a plane. 6. General equation of a plane. Position and metric problems in E3. 7. Vector function of one real variable. Definition and equation of a curve, tangent. Accompanying trihedron , flection and torsion. 8. Helix. Equation, basic properties. Constructive problems. 9. Surface, curves on a surface, tangent plane. 10. Surface of revolution (sr), meridian, tangent plane. 11. Constructive problems, plane section, intersection. 12. Helicoids. Definition, basic properties and constructive problems. 13. Cyclic helicoids. Ruled helicoids. 14. Revision.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 56 hours per semester
- Preparation for credit
- 28 hours per semester
- Preparation for exam
- 28 hours per semester
- Home preparation for classes
- 8 hours per semester
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Learning outcomes
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The objectives of the course in terms of learning outcomes and competencies is to acquaint students with the basics of mapping spatial objects into a plane (Monge projection), with the basics of analytical geometry in E3, with the basic theoretical knowledge of rotational and screw surfaces, including their applications and constructive tasks in Monge projection.
Basic theoretical knowledge and constructive skills of descriptive geometry (Monge projection) and differential geometry of curves and surfaces.
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Prerequisites
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Knowledge of the secondary school geometry and mathematics, knowledge of the differential calculus of one real variable.
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Assessment methods and criteria
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Combined examination
Presence in seminars, 3 tests, 2 drawings.
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Recommended literature
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Kargerová, M.:. Deskriptivní geometrie pro technické školy. Ostrava, Montanex, 1997.
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Pecina, V. - Přívratská J.:. Geometrie pro techniky - modul 1. Liberec, TU, 2001.
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Pecina, V. - Přívratská J.:. Geometrie pro techniky - modul 2. Liberec, TU, 2002.
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Pecina, V. - Přívratská J.:. Geometrie pro techniky - modul 3. Liberec, TU, 2003.
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Pomykalová, E.:. Matematika pro gymnázia - stereometrie. Praha, Prometheus, 1995.
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Urban, A.:. Deskriptivní geometrie I, II. Praha, SNTL, 1967.
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