|
Lecturer(s)
|
-
Chodorová Marie, RNDr. Ph.D.
-
Rachůnek Lukáš, doc. RNDr. Ph.D.
|
|
Course content
|
Course Content Fundamentals of solid geometry: positional and metric properties, surfaces and solids. Representation of space: principles of projection, parallel and orthogonal projection. Projective extension of Euclidean space: points at infinity. Affinity and collineation: properties and applications. Contour (height) projection: theoretical foundations. Representation of a point, line, and plane in contour projection. Positional problems in contour projection. Metric problems in contour projection. Representation of polyhedra. Problems involving polyhedra. Practical applications of contour projection.
|
|
Learning activities and teaching methods
|
|
Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
|
|
Learning outcomes
|
The aim of the course is to introduce students to the fundamentals of solid geometry and the representation of three-dimensional objects in the plane, with an emphasis on projection methods and solving problems involving polyhedra. Students will: understand the basic concepts of solid geometry (positional and metric properties), acquire the principles of representing spatial objects in the plane, learn to work with parallel and orthogonal projection, understand the projective extension of space and the role of points at infinity, become familiar with affinity and collineation and their use in geometric problems, develop skills in contour (height) projection, learn to represent basic polyhedra, gain proficiency in solving positional and metric problems involving solids.
After completing the course, the student will have: Knowledge: understands the basic concepts of solid geometry and descriptive geometry, knows the principles of representing spatial objects in the plane, understands the properties of parallel and orthogonal projection, understands the projective extension of Euclidean space and the role of points at infinity, knows the properties of affinity and collineation and their geometric meaning, understands the principles of contour (height) projection and its applications. Skills: is able to represent basic geometric objects and solids using various projection methods, can solve positional and metric problems in solid geometry, applies affinity and collineation in solving geometric problems, is able to work with contour projection when representing points, lines, and planes, can analyze and solve problems involving polyhedra. Competences: is able to independently solve basic problems in descriptive geometry and solid geometry, can connect spatial imagination with geometric constructions, is able to apply acquired knowledge to practical problems of representation, understands the relationships between geometric properties of objects and their representation in the plane.
|
|
Prerequisites
|
unspecified
|
|
Assessment methods and criteria
|
Written exam, Student performance, Analysis of Activities ( Technical works)
o successfully complete the course, the student must: regularly attend tutorials, demonstrate understanding of the basic concepts of solid geometry and projection methods, be able to solve positional and metric problems, be able to represent basic geometric objects and solids, apply affinity and collineation in problem solving, meet continuous assessment requirements (two midterm tests), obtain course credit.
|
|
Recommended literature
|
-
Machala F., Sedlářová M., Srovnal. (2002). Konstrukční geometrie. Olomouc.
-
Piska R. Medek M. (1966). Deskriptivní geometrie I. Praha.
-
Pomykalová, E. (2012). Deskriptivní geometrie pro SŠ. Prometheus.
-
Urban A. (1949). Deskriptivní geometrie I. Praha.
|