Geometric interpretation and visualization of particular geometric concepts at metric spaces study

Abstract

The paper considers the issues of studying method of geometric properties of metric spaces. These questions arise when students learn the basic concepts of the metric spaces theory. Difficulty in the concepts understanding arises due to the lack of the geometric interpretation or appropriate visualization. To build a geometric interpretation of rectilinear and flat placement of points of metric space, it is proposed to build the appropriate analogues in two-dimensional and three-dimensional arithmetic Euclidean spaces. To visualize these concepts, it is proposed to use a dynamic geometric environment GeoGebra 3D. This approach allows to demonstrate both the similarity of individual geometric concepts of metric space with the corresponding concepts of Euclidean geometry, and cases of the "non-Euclidean". The study is useful for teachers and students of higher education institutions majoring in physics and mathematics. Some examples can be used in the study of basic geometric concepts by students of secondary education, in-depth study of mathematics and in various types of informal education.