К вопросу о методике использования алгоритмов при решении задач начертательной геометрии

Abstract

In this paper the urgent problem of the formal approach to the teaching of descriptive geometry (DG) has been formulated. The authors consider the algorithm concept and approaches to formal description of methods (algorithms) for tasks solving. It is emphasized that the known methods for creating and presenting of algorithms for DG tasks solving do not reflect all possibilities of algorithmization as it is. In the third section the authors, in examples, emphasize the complexity of DG tasks solutions algorithmization. The diversity of solutions for one or another DG task is noted depending on location of initial figures that requires a suitable context analysis in solving, and, as a consequence, the algorithm choice. It is pointed out that the reason for this is different ways for expressing of figures’ geometric properties by means of drawing. General algorithms for applying the method of loci and geometric transformations to tasks solving are considered. From the loci position have been considered two basic tasks of DG: plotting a point drawing in the coordinates, and a perpendicular to the plane. The method of loci importance is emphasized in view of algorithms compilation simplicity and wide possibilities for tasks solving. The authors note that algorithmization does not reduce the importance of geometry knowledge or understanding of the tasks geometric content and used methods, but emphasizes the importance of the first stage for tasks solving — the stage of analysis at which basic decisions are made and its method is chosen. In conclusion it is emphasized that in the practice related to solving of DG educational tasks it is optimal to apply the algorithmization in point, as it enables to structure the course, operate with compact algorithms, and introduce automated technologies of constructive geometric modeling.