DEVELOPMENT OF SPATIAL THINKING OF MASTER STUDENTS WHEN STUDYING NON-EUCLIDEAN GEOMETRY (PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE KYRGYZ REPUBLIC, 2024)
This article says that the concepts of non-Euclidean geometries (Lobachevsky’s geometry, Riemann’s geometry) can contribute to the development of spatial thinking undergraduates-future teachers of mathematics. Here the fifth postulate of Euclid is given, the emergence of non-Euclidean geometry, a brief summary of Lobachevsky’s geometry and Riemann’s geometry are shown. The connections and features of the geometries of Euclid, Lobachevsky and Riemann, which are called “three great geometries”, are reflected. It is concluded that the spatial thinking of students at any age can be developed in the process of teaching with the help of specially organized conditions, influencing them systematically. One of the special conditions for undergraduates is didactic materials on Euclidean and non-Euclidean geometry. When establishing connections and differences between these three geometries, as well as in the formation of spatial thinking of undergraduates, it is effective to consider the concepts of these geometries in parallel, and not separately in each of them. The methodology presented in the article for introducing the basic concepts of non-Euclidean geometry was implemented at lectures and practical classes in geometry at Osh State University with undergraduates. This made it possible to increase the efficiency of the development of their spatial thinking.
Keywords: V postulate; Euclid’s geometry; parallel lines; Lobachevsky’s geometry; Riemann’s geometry; spatial thinking; undergraduates