NonEuclidean Geometry

NonEuclidean Geometry

1st Edition - January 1, 1964

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  • Author: Herbert Meschkowski
  • eBook ISBN: 9781483259215

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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

Product details

  • No. of pages: 112
  • Language: English
  • Copyright: © Academic Press 1964
  • Published: January 1, 1964
  • Imprint: Academic Press
  • eBook ISBN: 9781483259215

About the Author

Herbert Meschkowski

About the Editors

D. Allan Bromley

Nicholas Declaris

W. Magnus

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