Features Of Teaching Applied Geometry of Surfaces of Special Classes

Abstract

Teaching geometric and graphic disciplines, which include descriptive geometry and engineering graphics, at a technical university is often associated with some difficulties. Displaying spatial objects in a drawing requires a student to have basic knowledge of geometry, a developed spatial representation, accuracy, and patience. For teachers, the problem of finding effective methods for diagnosing gifted students, as well as overcoming unfavorable socio-psychological conditions for personal development, is urgent. Both cognitive and creative components of the educational process are of great importance in the formation of professional and general cultural competencies of students (future engineers).

In order to develop students ' creative component in the process of studying geometric and graphic disciplines, the authors propose their own methodology for teaching applied geometry of surfaces, based on an epistemological scheme with an emphasis on the creative development of the theory of transformations. The didactic components in this case include: particular types of linear transformations of space (linear-homogeneous transformations), analytical and graphical methods for determining them, an algorithm for the continuous process of constructing corresponding points in a linear-homogeneous transformation and its graphical interpretation, instantaneous linear-homogeneous transformations, their main properties and application in the design of airfoil surfaces, a combined method for setting linear-homogeneous transformations, theoretical substantiation of the existence of various geometric systems with the theory of groups and transformation invariants, practical applications in the field of designing technical forms of surfaces of a special class, including for aviation purposes, based on linear-homogeneous instantaneous transformations.

The practical significance of the results lies in the possibility of using the proposed methodology for teaching certain topics of geometric and graphic disciplines in the preparation of engineering students. The method was tested at the Moscow Aviation Institute at the Department of Engineering Graphics.