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What is Hyperbolic Plane

Chapter 7
NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World
Also knows as the Bolyai-Lobachevsky plane , it is the geometric structure of dimension 2 such that given a line and an external point, there are at least two parallel lines to the aforementioned one, which contain the point.
Published in Chapter:
“NeutroGeometry Laboratory”: The New Software Dedicated to Finite NeutroGeometries
Erick González Caballero (Technological University of Havana, Cuba)
Copyright: © 2023 |Pages: 25
DOI: 10.4018/978-1-6684-4740-6.ch007
Abstract
Mixed projective-affine-hyperbolic (MPAH) planes belong to both the branches of NeutroGeometries and mixed or Smarandache geometries. This kind of plane is a geometric structure containing a finite number of points. Some lines of the MPAH satisfy the axioms of projective planes, other lines satisfy the axioms of affine planes, and others satisfy the axioms of hyperbolic planes. Therefore, each of the axioms of parallelism is partially satisfied. This chapter describes version 1.0 of a new software called “NeutroGeometry Laboratory” coded in Python by the author that is used for the calculation and visualization related to MPAH planes. This software is easy to use by users once they know the theory of finite mixed projective-affine-hyperbolic planes, and particularly, it supports the study of this topic and finite planes in general.
Full Text Chapter Download: US $37.50 Add to Cart
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Chapter 8
A Constructive Introduction to Finite Mixed Projective-Affine-Hyperbolic Planes
Also known as the Bolyai-Lobachevsky plane , it is the geometric structure of dimension 2 such that given a line and an external point; there are at least two parallel lines to the aforementioned one, which contain the point.
Published in Chapter: A Constructive Introduction to Finite Mixed Projective-Affine-Hyperbolic Planes; From: NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World
Full Text Chapter Download: US $37.50 Add to Cart
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