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.
Way of continuous check of knowledge in the course of semester
Course credit
========================================================
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
========================================================
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
========================================================
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
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction