New special points of triangles in connection with gnomonic projections of crystallographic complexes

Abstract

There is a large number of special points, the position of which is strictly deduced for each given trigon. These points are discovered when studying certain properties of trigons, the number of which is very significant. Despite the simplicity of such an image as an ordinary trigon, its study is still not yet can be considered exhausted and over time, although rarely, new and new properties are discovered. The task is to find the point that serves as the center of the linear primacy of the rays—the polars of the points of the circumscribed circle. To solve this problem, it is enough to find the polars of any two points of the circle in relation to the triangle; the point of their intersection is the desired one. It is this point that constitutes the new special point of the triangle that is mentioned in the title.