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.
Keywords:
absolute geometry, inversion, Lobachevskii geometry, horocycle, Poincaré model, pencil of circles, equidistant curve.