714-0375/06 – Constructive Geometry (KG)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
| Subject guarantor | Mgr. František Červenka | Subject version guarantor | Mgr. Dagmar Dlouhá, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2010/2011 | Year of cancellation | 2018/2019 |
| Intended for the faculties | FS | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
• 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
Teaching methods
Lectures
Individual consultations
Tutorials
Summary
Focus properties of conic sections. The two-plane method. Perspective affinity.
Orthogonal axonometry. Orthogonal image of circle. Prismatic surface.
Cylindrical surface. Pyramidal surface. Conical surface. Central collineation.
Spherical surface. Surfaces of rotation. Quadrics of rotation. One-sheet
hyperboloid of rotation. Circular helix. Spiral surfaces.
Compulsory literature:
Recommended literature:
1/ Plocková, E. - Řehák, M.: Sbírka řešených příkladů z DG a KG, díl 3. -
Mongeovo promítání. Skriptum VŠB - TU, Ostrava 1995.
2/ Stejskalová, J. - Vrbenská, H.: Sbírka řešených příkladů z DG a KG, díl 4. -
Axonometrie. Skriptum VŠB - TU, Ostrava 1995.
3/ Urban, A.: Deskriptivní geometrie I, II, Praha, SNTL, 1967.
4/ Doležal, M. - Poláček, J. - Tůma, M.: Sbírka řešených příkladů z DG a KG,
díl 5. - Rotační a šroubové plochy. Skriptum VŠB - TU, Ostrava 1995.
Additional study materials
Way of continuous check of knowledge in the course of semester
Course credit
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To obtain a credit the student has to submit 3 drawings. Student can get 12 points for attendance of the lectures and another 8 points for properly solved homework. A maximum of 20 points.
Exam
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Written part of an exam is classified by 0 - 60 points. The part is successful if student obtains at least
25 points.
Oral part of the exam is classified by 0 - 20 points. The part is successful if student obtains
at least 5 points.
Point quantification in the interval 100 - 91, 90 - 81, 80 - 71, 70 - 61, 60 - 51, 50 - 0
ECTS grade A B C D E F
Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0
National grading scheme excellent very good satisfactory failed
A set of topics for the theoretical part of the exam
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1) Monge projection – position tasks.
2) Monge projection - metric tasks.
3) Orthogonal axonometry - basic position tasks.
4) Orthogonal projection of a circle (Rytz construction).
5) Monge projection - views of a circle in a general plane.
6) Prism surface – cut by a plane.
7) Cylindrical surface – cut by a plane.
8) Pyramid surface – cut by a plane.
9) Construction of a sphere, cut of a sphere by a plane, intersection of line and solid.
10) Focal properties of conics - ellipse, hyperbola, parabola.
11) Construction of conics.
12) Surfaces of revolution - development, application, construction of the tangent plane.
13) Surfaces of revolution - quadrics - development, application, construction of the tangent plane.
14) Intersections of surfaces of revolution.
15) Intersections of quadrics.
16) Design and layout of helix.
17) Screw ruled surfaces - the classification, tangent plane.
E-learning
http://www.studopory.vsb.cz (in Czech)
Other requirements
No more requirements.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
I Introduction to constructive geometry, axial affinity, Monge projection – position tasks,
Monge projection - metric tasks
II Orthogonal axonometry - basic position tasks, Orthogonal projection of the circle (trammel construction, Rytz construction)
III Views of circle in the projection plane (ax.) and in a general plane (MP), Prism surface, cylindrical surface – cut by a plane
IV Central collineations, pyramid surface – cut by a plane
V Conical surface, sphere – cut by a plane perpendicular to the projection plane, Intersections of a line and solids
VI Helix, screw surfaces, Surfaces of revolution - creation, application, Intersections of surfaces of revolution
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction