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

Authors

  • Jinan F. Al-Jobory Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq

Keywords:

Axiomatic system, Finite hyperbolic plane (finite Bolyai-Lobachevsky plane), Finite hyperbolic geometry (finite Bolyai-Lobachevsky geometry), The undefined terms (point and line), Parallel lines, Incident

Abstract

In this paper, two important models for the finite hyperbolic plane (finite Bolyai-Lobachevsky plane) Bn,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.

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Published

2022-12-31

Issue

Section

Articles

How to Cite

(1)
Some Models of the Finite Hyperbolic Geometry and the Finite Hyperbolic Plane. ANJS 2022, 25 (4), 59-62.