Teaching of Academic Subjects

Subject: Descriptive Geometry and Didactics of Descriptive Geometry

1. Orthogonal projection (Dimensioned and Monge’s projection, Orthogonal axonometry, Topography – principles of projection, basic constructions, applications).
2. Oblique projection (Oblique-angle projection, Oblique axonometry – principles of projection, basic constructions, applications).
3. Central projection (Central projection, Linear perspective, Perspective axonometry – principles of projection, basic constructions, applications).
4. Perspective affinity. Use of projection in solving various problems in descriptive geometry. Planar sections of prismatic and circular cylindrical surfaces.
5. Perspective collineation. Use of projection in solving problems in descriptive geometry. Planar sections of pyramidal and circular conical surfaces.
6. Spherical surface. Methods for solving positional problems on a spherical surface. Illustration of solutions using the method of rectangular axonometry. Oblique projection of a spherical surface.
7. Photogrammetry. Elements of internal and external orientation of an image. Reconstruction from one orthogonal and one oblique image.
8. Classification and principles of cartographic projections (planar, cylindrical, conical, others). Planar cartographic projections (orthographic, stereographic, gnomonic).
9. The method of axonometry and linear perspective in projection equations.

1. Projective construction of point and line conics. Pascal’s and Brianchon’s theorems and their practical applications.
2. Perspective and projective mappings in the extended Euclidean plane. Determination, basic properties. Fundamental theorem of projective mapping.
3. Parametric representation of a curve in E₂ and E₃, Frenet trihedron. Natural parametrisation of a curve. Curvature and osculating circle of a curve.
4. Parametric representation of a surface in E₃, curve on a surface, tangent plane of a surface. Normal curvature of a surface.
5. Algebraic plane curves, common points of a curve and a line. Classification of points, tangential forms.
6. Common points of two plane algebraic curves, resultant. Bézout’s theorem.
7. Modelling surfaces from a generatrix curve using classes of geometric transformations.

1. The relationship of the didactics of descriptive geometry to other scientific disciplines.
2. Objectives of teaching descriptive geometry and technical drawing.
3. Curriculum design for descriptive geometry.
4. Analysis and synthesis in teaching descriptive geometry.
5. Concept formation process in teaching descriptive geometry and some typical errors in acquiring concepts in descriptive geometry.
6. Basic concepts of the theory of didactic situations and their utilisation in descriptive geometry.
7. Axioms, definitions, and theorems in descriptive geometry.
8. Direct proof, indirect proof, and proof by contradiction and their use in descriptive geometry.
9. Preparation of didactic situations in descriptive geometry.