# A Simple Non-Euclidean Geometry and Its Physical Basis

## An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity

• Editors
• BasilĀ Gordon

Part of the Heidelberg Science Library book series (HSL)

1. Front Matter
Pages i-xviii
2. Basil Gordon
Pages 1-32
3. Basil Gordon
Pages 33-76
4. Basil Gordon
Pages 77-157
5. Basil Gordon
Pages 158-213
6. Back Matter
Pages 214-307

### Introduction

There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflecĀ­ tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "non-uniqueness" of geometry; of the existence of many geometric systems.

### Keywords

DEX Heidelberg Mathematica Nichteuklidische Geometrie Non-Euclidean Geometry curvature duality eXist form functions geometry hyperbolic geometry language mathematics transformation

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-6135-3
• Copyright Information Springer-Verlag New York 1979
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-90332-3
• Online ISBN 978-1-4612-6135-3
• Series Print ISSN 0073-1595