Lobachevskian algebraic distance in geometry with the Poincaré half-plane model and some applications

Abstract

In this paper we present the concept of axis and Lobachevskian algebraic distance of the directional segmental-arcs, and then find the relationship between the Lobachevskian line segments created by intercepting the axes on two fixed Lobachevskian lines. The results we obtained are Theorem 2.1, Theorem 2.2 and Corollary 2.3.

Keywords: Lobachevskian algebraic distance, directional segmental-arc, Poincaré half-plane model, Lobachevskian line segment, Lobachevskian line.