FORMATION OF THE CONCEPT OF ANGLE BY MEANS OF METRIC GEOMETRY ON GEOMETRIC MATERIAL OF 9TH GRADE

Abstract

The work is to study the possibility of using the means of metric geometry for the formation of basic geometric concepts in the study of geometry in secondary education. The use of metric geometry opens the way for students to get acquainted with the elements of non-Euclidean geometries on both intuitive and axiomatic levels. In the paper, an alternative definition of the rectilinear placement of points is given based on the definition of the numerical characteristic of the angle formed by the three points of the metric space. With the help of numerical characteristics, it is easy to obtain definitions of right and straight angles. The material presented in this paper can be used in geometry lessons starting from the 9th year and in extracurricular activities with students studying in classes with in-depth mathematics learning.

Formulation of the problem. The material of this work relates mainly to the teaching of mathematics in classes with in-depth mathematics learning. The current mathematical education state raises the question of the need to acquaint students with the basic concepts and facts of non-Euclidean geometries. Doing this directly by referring to the actual material about such geometries is quite difficult because of the significant level of its formalization. To address this issue, the authors offer to use the means of metric geometry as the closest to the school course of geometry. It is offered to begin this work with the formation of generalized basic geometric concepts and objects, such as a point, an angle, and a rectilinear placement of points.

Materials and methods. The results are based on the analysis of existing textbooks in mathematics for classes with in-depth study, textbooks on geometry and mathematical analysis of higher education institutions, scientific publications and tested when reading the relevant special course for students majoring in "014.04 Secondary Education (Mathematics)" master's degree.

Results. Based on the proposed definition of the angle as an ordered triple of points, analogs of classical geometric relations are obtained. These analogues allow the demonstration of elements of non-Euclidean geometries by means of elementary geometry.

Conclusions. The analytical apparatus of metric geometry makes it possible to form a generalized understanding of basic geometric concepts, such as point, angle, distance between points, rectilinear placement of points.