Some Models of the Finite Hyperbolic Geometry and the Finite Hyperbolic Plane

Abstract

In this paper, two important models for the finite hyperbolic plane (finite Bolyai-Lobachevsky plane) B_n,m will be given, the first model is when n = 3 and m = 3, while the second model is when n = 3 and m = 4.

    Also, two important models for the finite hyperbolic geometry (finite Bolyai-Lobachevsky geometry) are given, the first model is when each line contains either 4 or 3 distinct points and each point is on 6 distinct lines, while the second model is when each line contains either 3 or 2 distinct points and each point is on either 7 or 8 lines. All models are represented in a simple form, which help the readers and researchers to understand the different facts about the finite Bolyai-Lobachevsky plane and the finite Bolyai-Lobachevsky geometry.