NonEuclidean Geometry - 1st Edition - ISBN: 9781483256641, 9781483259215

NonEuclidean Geometry

1st Edition

Authors: Herbert Meschkowski
Editors: D. Allan Bromley Nicholas Declaris W. Magnus
eBook ISBN: 9781483259215
Imprint: Academic Press
Published Date: 1st January 1964
Page Count: 112
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Description

Noneuclidean Geometry focuses on the principles, methodologies, approaches, and importance of noneuclidean geometry in the study of mathematics.

The book first offers information on proofs and definitions and Hilbert's system of axioms, including axioms of connection, order, congruence, and continuity and the axiom of parallels. The publication also ponders on lemmas, as well as pencil of circles, inversion, and cross ratio.

The text examines the elementary theorems of hyperbolic geometry, particularly noting the value of hyperbolic geometry in noneuclidian geometry, use of the Poincaré model, and numerical principles in proving hyperparallels. The publication also tackles the issue of construction in the Poincaré model, verifying the relations of sides and angles of a plane through trigonometry, and the principles involved in elliptic geometry.

The publication is a valuable source of data for mathematicians interested in the principles and applications of noneuclidean geometry.

Table of Contents


Preface

Chapter 1 On Proofs and Definitions

Chapter 2 Hilbert's System of Axioms

I. Axioms of Connection

II. Axioms of Order

III. Axioms of Congruence

IV. Axioms of Continuity

V. The Axiom of Parallels

Chapter 3 From the History of the Parallel Postulate

Chapter 4 Lemmas

I. Pencil of Circles

II. Inversion

III. Cross Ratio

Chapter 5 The Poincaré Model

Chapter 6 Elementary Theorems of Hyperbolic Geometry

Chapter 7 Constructions

Chapter 8 Trigonometry

Chapter 9 Elliptic Geometry

Chapter 10 Epilog

References

Index

Details

No. of pages:
112
Language:
English
Copyright:
© Academic Press 1964
Published:
Imprint:
Academic Press
eBook ISBN:
9781483259215

About the Author

Herbert Meschkowski

About the Editor

D. Allan Bromley

Nicholas Declaris

W. Magnus

Ratings and Reviews