Abstract: The group of motions of the Lobachevskii plane, as well as that of the Euclidean plane, is generated by reflections in straight lines.This allows ones to develop an approach to constructing the Poincaré model of Lobachevskii plane based on the properties of inversions and pencils of circles in the Euclidean plane.

Abstract:

In the paper, we develop some approaches to teaching multidimensional geometry in elective courses the aim of which is to help students to develop multidimensional geometric intuition. Special attention is given to the use of transformation groups in the study of geometry of regular polyhedrons.

Abstract:

The aim of the paper is to demonstrate how the techniques of one of the geometries indicated in the title can be used for solving problems formulated in the framework of one of the other geometries. In particular, it is shown how problems formulated in the framework of affine or projective geometry can be solved with an appropriate choice of Euclidean scalar product.