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The Foundations of Geometry and the Non-Euclidean Plane

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Cover of 'The Foundations of Geometry and the Non-Euclidean Plane'

Table of Contents

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    Book Overview
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    Chapter 1 Equivalence Relations
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    Chapter 2 Mappings
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    Chapter 3 The Real Numbers
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    Chapter 4 Axiom Systems
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    Chapter 5 Models
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    Chapter 6 Incidence Axiom and Ruler Postulate
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    Chapter 7 Betweenness
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    Chapter 8 Segments, Rays, and Convex Sets
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    Chapter 9 Angles and Triangles
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    Chapter 10 The Golden Age of Greek Mathematics
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    Chapter 11 Euclid’s Elements
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    Chapter 12 Pasch’s Postulate and Plane Separation Postulate
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    Chapter 13 Crossbar and Quadrilaterals
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    Chapter 14 Measuring Angles and the Protractor Postulate
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    Chapter 15 Alternative Axiom Systems
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    Chapter 16 Mirrors
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    Chapter 17 Congruence and the Penultimate Postulate
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    Chapter 18 Perpendiculars and Inequalities
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    Chapter 19 Reflections
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    Chapter 20 Circles
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    Chapter 21 Absolute Geometry and Saccheri Quadrilaterals
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    Chapter 22 Saccheri’s Three Hypotheses
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    Chapter 23 Euclid’s Parallel Postulate
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    Chapter 24 Biangles
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    Chapter 25 Excursions
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    Chapter 26 Parallels and the Ultimate Axiom
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    Chapter 27 Brushes and Cycles
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    Chapter 28 Rotations, Translations, and Horolations
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    Chapter 29 The Classification of Isometries
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    Chapter 30 Symmetry
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    Chapter 31 Horocircles
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    Chapter 32 The Fundamental Formula
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    Chapter 33 Categoricalness and Area
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    Chapter 34 Quadrature of the Circle
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Title
The Foundations of Geometry and the Non-Euclidean Plane
Published by
Springer New York, December 2012
DOI 10.1007/978-1-4612-5725-7
ISBNs
978-1-4612-5727-1, 978-1-4612-5725-7
Authors

Martin, George E.