RELATIVITY AND NUMERICAL TRIANGLES

Abstract

Additional new properties of the triangle, which is one of the main and most important figures in plane geometry are investigated. Points of a certain plane are considered and for three given base points A, B, and C of this plane, the following definitions are introduced: point X is called triangular relative to the base points if there exists a triangle with side lengths |XA|, |XB| and |XC|; an ordered triple of numbers (a, b, c) is called a numerical triangle relative to the base points if there exists a point X that is triangular relative to the base points, so that |XA| = a, |XB| = b and |XC| = c. For the given base points, two problems are studied: finding triangular points and numerical triangles relative to the base points. Only the case where all three base points A, B and C lie on the same straight line is considered, with point B located on the segment AC. It is assumed that this line is the x-axis, and that point B coincides with the origin. Under this assumption, the set of triangular points relative to the base points becomes symmetric with respect to the x-axis. Four possible configurations of these points are distinguished:1) all three base points coincide; 2) only two base points A and B coincide; 3) the general case of distinct base points where |AB| > |BC|; 4) the special case of distinct base points where |AB| = |BC|. For each of these cases the set of triangular points relative to the base points of the plane is demonstrated; the set of triangular points on the x-axis and the corresponding set of numerical triangles are described. Attention is also drawn to the interdisciplinary function of the category of relativity, particularly within the language system.