Open AccessElements of non-Euclidean geometry in the formation of the concept of rectilinear placement of points in schoolchildren
Author(s) -
Валерій Кузьмич,
Liudmyla Kuzmich
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1840/1/012004
Subject(s) - euclidean geometry , metric (unit) , non euclidean geometry , mathematics , axiom , set (abstract data type) , euclidean space , space (punctuation) , geometry , work (physics) , metric space , algebra over a field , mathematics education , pure mathematics , computer science , engineering , operations management , programming language , operating system , mechanical engineering
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 7 th – 9 th 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 10 th – 11 th 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.