Elements of non-Euclidean geometry in the formation of the concept of rectilinear placement of points in schoolchildren

Abstract

The paper deals with issues of the metric geometry basics. In particular, the concept of rectilinear placement of points is considered, based on the axioms of the distance between two points of metric space. This approach allows forming a modern view of the property of straightness in the pupils. This paper analyzes the content of existing mathematics textbooks for general educational institutions to acquaintance of pupils with the elements of metric geometry. The first part of the paper provides information about the rectilinear placement of points; it can be used in Geometry lessons in the 7th – 9th grades. Set of linear functions are considered as examples of points of metric space. The similar work was done in the second part of the work for geometric material of the 10th – 11th grades. In addition, some simple examples of metric spaces that may be accessible to pupils of the relevant classes are discussed. The purpose of the work is gradually introduction of pupils to the elements of non-Euclidean geometries, to form a generalized notion of the distance between the points and rectilinear of their placement. The work can be used for Mathematics teaching at school and for retraining of teachers of Mathematics.

1st Symposium on Advances in Educational Technology: Outlook

“…This article highlights further research by the authors, begun in [120,300,304]. The analysis of four curricula of teachers training of natural sciences in higher education institutions is presented in the article "Analysis and prospects of the future teachers training of the integrated course "Natural sciences"" [303] by Nataliia V. Valko (figure 79) and Viacheslav V. Osadchyi.…”

Application of non-Euclidean metric in the electric power industry for reduction of measurement uncertainty

“…One of the directions of the search for such a generalizing parameter is the use of a metric different from the Euclidean metric in the space of complex electrotechnical parameters. Quite often, various non-Euclidean metrics are used to solve different tasks [2][3][4][5][6][7][8][9][10][11][12]. These can be linear non-Euclidean metrics for which   is a quadratic function, etc [8].…”

“…Non-Euclidean geometry is a relatively new and powerful mathematical apparatus, which is currently used for analysis and calculations in the field of automation and robotics [2][3][4], in physics [5,6], medicine [7,8], information technologies [9][10][11], the educational process [12], and other fields of science. Recently, non-standard methods of analyzing processes in electric circuits and networks have been actively developed [13,14].…”

XII International Conference on Mathematics, Science and Technology Education: conference report

“…The article "Elements of non-Euclidean geometry in the formation of the concept of rectilinear placement of points in schoolchildren" [23] of Valerii I. Kuz'mich et al deals with issues of the metric geometry basics. In particular, the concept of rectilinear placement of points is considered, based on the axioms of the distance between two points of metric space.…”