ОРТОГОНАЛЬНЕ ПРОЄКЦІЮВАННЯ В ЗАДАЧАХ СТЕРЕОМЕТРІЇ

Abstract

The article reveals one of the methods of activity of the subject of education, demonstrates a heuristic prescription, which it is advisable to use by drawing up a plan and solving many problems of stereometry, in particular, by a graphic or graphical-analytical method. This is an unconventional transformation within the stereometric body – “internal projection” – an imaginary spatial transformation that makes it easier for a binary image of the body to perpendicular to a straight line (or to a plane), the common perpendicular of two crossed straight lines, to postpone an angle with given degree measure, etc. There are conical and cylindrical internal projection. As a rule, the first of them is advisable to apply in the case of a pyramid and a cone, and the second – a prism and a cylinder. The plane of the projections and the direction of internal projection is chosen by the student. The success in obtaining the result depends on how successfully these two components of the projection apparatus are selected. If, for example, you need to build a common perpendicular of two intersecting straight lines (see task 1), then the essence is that the projection direction is parallel to one of them, and the projection plane is perpendicular to this straight line. Sometimes it happens that the plane of projections contains another straight line or is located in space parallel to the latter. Further, according to the statement of the theorem on the projection of a right angle, the segment of the common perpendicular and the right angle between it and the second straight line are projected onto the entered plane in full size. "Reverse projection" build the image of the desired common perpendicular. We have considered only examples where the plane of projections is the base of the stereometric body (tasks 1-3), and the direction of projection is perpendicular to the base Exception is the task 3, especially when the straight lines a, b and c intersect at their common point S projection. Keywords: stereometric body; picture; internal orthogonal projection; positional, metric tasks; constructive method.