A SCHOOL MATHEMATICS COURSE: THE CONCEPT OF FIGURES

Abstract

The article draws attention to the method of forming an important mathematical concept – the distance between two geometric figures – in students of a senior specialized school. Students are introduced to the concept of distance from a point to a straight line, from a point to a plane, first in planimetry lessons, and then in stereometry lessons. In the case when other figures are considered – segment, ray, circle, triangle, parallel lines, parallel lines and planes, etc., they do not possess such concepts, as practice shows. They often use intuitive ideas that lead to mistakes when solving problems or proving theorems. If high school students form a generalization of the concept of the distance between figures, then using it, they will be able to establish what will be the expression of the distance between figures, different from those already known to them.

The article shows how from the general definition of the distance between figures the following definitions follow: a) the distance from a point to a figure; from a point to a straight line, line, segment, plane, ray, which is an expression of such a distance; b) distances between parallel and passing lines, between a line parallel to the plane; between parallel planes, which is an expression of such a distance.

Recommendations are offered for substantiating what will be the distance between the figures that are distant from the considered ones.

The application of the given definitions is illustrated by examples of solving two problems in geometry and one in algebra and the beginnings of analysis. It is emphasized that such justifications are an integral part of solving the problem, because, according to the requirements, the solution of each mathematical problem should be correct, complete, justified and, if possible, rational.

The article is addressed to teachers of mathematics, authors of school textbooks on mathematics, students-future teachers of mathematics.