Course detail

# Constructive Geometry

Perspective collineation and affinity,circle in affinity. Coted projection, topographic surfaces, theoretical solution of the roofs, orthogonal axonometry and linear perspective.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Students should be able to construct conics using their focus properties, perspective colineation and affinity. Understand and get the basics of projection: coted, Monge`s projection, orthogonal axonometry, and linear perspective. They should be able to solve simple 3D problems, display the basic geometric bodies and surfaces in each projection, their section. In a linear perspective, they should be able to draw a building. They construct a helix using specified elements, an orthogonal closed rule right helicoidal surface. They construct a hyperbolic paraboloid, circle and parabolic conoid using specified elements.

Prerequisites

Basics of plane and 3D geometry a stereometrie as taught at secondary schools.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

1. Introduction - principles of parallel and central projection. Perspective collineation and affinity-basic properties.
2. System of basic problems, examples. Coted projection. Basic problems.
3. Coted projection. Basic problems.
4. Coted projection. Monge`s projection.
5. Orthogonal axonometry.
6. Orthogonal axonometry.
7. Basic parts of central projection. Linear perspective.
8. Linear perspective.
9. Linear perspective. Topographic surfaces (basic concepts and constructions).
10. Topographic surfaces.
11. Topographic surfaces. Theoretical solution of the roofs.
12. Theoretical solution of the roofs.
13. Questions.

Aims

Students should be able to construct conics using their focus properties, understand the principles of perspective colineation and affinity using such properties in solving problems, understand and get the basics of projection: Monge`s projection, orthogonal axonometry, and linear perspective. They should develop 3D visualization and be able to solve simple 3D problems, display simple geometric bodies and surfaces in each type of projection, their section with a plane and intercestions with a straight line. In a linear perspective, they should be able to draw a building. They should learn the basics of the theory of curves and surfaces, construct a helix using specified elements as well as an orthogonal closed rule right helicoidal surface. They should learn the basics of the theory of warped surfaces, construct a hyperbolic paraboloid, circle and parabolic conoid using specified elements.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Classification of course in study plans

• Programme B-P-C-SI (N) Bachelor's

branch VS , 1. year of study, summer semester, 5 credits, compulsory

• Programme B-K-C-SI (N) Bachelor's

branch VS , 1. year of study, summer semester, 5 credits, compulsory

• Programme B-P-E-SI (N) Bachelor's

branch VS , 1. year of study, summer semester, 5 credits, compulsory

• Programme B-P-C-MI (N) Bachelor's

branch MI , 1. year of study, summer semester, 5 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Exercise

26 hours, compulsory

Teacher / Lecturer

eLearning