«ПОБУДОВИ» У ТРИВИМІРНОМУ ЕВКЛІДОВОМУ ПРОСТОРІ ТА ДОЦІЛЬНИЙ ХАРАКТЕР ЇХ ВИСВІТЛЕННЯ У НАВЧАЛЬНИХ КУРСАХ ЕВКЛІДОВОЇ СТЕРЕОМЕТРІЇ ЗА УМОВИ ПРАКТИКО-ОРІЄНТОВАНОГО НАВЧАННЯ

Abstract

The article is devoted to the comprehensive analysis of the concept of geometrical «constructions» in three dimension Euclidean space from the position of practical-orientated process of training. According to its grounds, the theory of «constructions» in Euclidean solid geometry in essence doesn’t differ from theories of plane geometry onto «constructions by the help of different tools», to begin of «a compass and a ruler». From the theoretical point of view, just as in Euclidean plane geometry, in Euclidean solid geometry the question is in creation the corresponding canonical prolongation of the chosen axiomatic basis of three dimension Euclidean space. The character of such canonical prolongation is determined by the purpose of its possible subsequent practical applications. Examples of canonical prolongations of axiomatic basis of Euclidean solid geometry that are agreed with the corresponding canonical prolongations of axiomatic basis of Euclidean plane geometry in the form of axiomatic basis of «a compass and a ruler» are pointed out in the article. Such axiomatic bases of the theory of «constructions» of three dimensional Euclidean space allow to achieve the concordance of «constructions by the help of a compass and a ruler» in pictures of geometrical figures received by the help of parallel projecting with «constructions» at Euclidean space on the base of these pictures. At a result of the conducted analysis, we come to conclusion that provided practical-orientated process of training it makes a sense to supplement the traditional content of the course of solid geometry at institutions of general secondary education with some questions devoted to «constructions» in solid geometry. It is clear that in such a case the level of deepening in the essence of the question must be approximately the same one as in the course of plane geometry at institutions of general secondary education according to the «constructions» in Euclidean plane «by the help of a compass and a ruler». Simultaneously, in the course of Euclidean plane geometry it is important to pay student’s attention to the existence of different theories of «constructions», «by the help of different tools», to throw light on the essence of natural preconditions of such existence. Undoubtedly, the corresponding material must also be added to the content of professional training at teachers’ training institutions of higher education the future mathematics’ teachers of institutions of general secondary education. Such questions directly concern the scientific grounds of the up to date courses of geometry at institutions of general secondary education.