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This classic text provides overview of both classic and hyperbolic geometries, placing the work of key mathematicians/ philosophers in historical context. Coverage includes geometric transformations, models of the hyperbolic planes, and pseudospheres. ** Mathematics General geometry Non-Euclidean Title page 3 Date-line 4 Dedication 5 CONTENTS 7 PREFACE 11 INTRODUCTION 19 1 EUCLID'S GEOMETRY 24 The origins of geometry 24 The axiomatic method 28 Undefined terms 29 Euclid's first four postulates 32 The parallel postulate 36 Attempts to prove the parallel postulate 39 The danger in diagrams 41 The power of diagrams 43 Review exercise 44 Exercises 45 Major exercises 49 Projects 53 2 LOGIC AND INCIDENCE GEOMETRY 56 Informal logic 56 Theorems and proofs 58 RAA proofs 60 Negation 62 Quantifiers 63 Implication 66 Law of excluded middle and proof by cases 67 Incidence geometry 68 Models 70 Isomorphism of models 74 Projective and affine planes 76 Review exercise 80 Exercises 81 Major exercises 83 Projects 86 3 HILRERT'S AXIOMS 88 Flaws in Euclid 88 Axioms of betweenness 90 Axioms of congruence 100 Axioms of continuity 111 Axiom of parallelism 120 Review exercise 121 Exercises 122 Major exerci

Who reads Euclidean and Non-euclidean Geometries : Development and History?

Author

Marvin Jay Greenberg

Publisher

W. H. Freeman & Company

Published

1993

Language

EN

ISBN

9780716724469

Category

mathematics

Subjects

Mathematics, History, Stem

Rating

3.5 / 5 (21 ratings)

Updated

2026-03-14