Book:Richard S. Millman/Geometry: A Metric Approach with Models/Second Edition
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Richard S. Millman and George D. Parker: Geometry: A Metric Approach with Models (2nd Edition)
Published $\text {1991}$, Springer Verlag
- ISBN 0-387-97412-1
Part of the Undergraduate Texts in Mathematics series.
Subject Matter
Contents
- Preface
- Computers and Hyperbolic Geometry
- CHAPTER 1: Preliminary Notions
- 1.1 Axioms and Models
- 1.2 Sets and Equivalence Relations
- 1.3 Functions
- CHAPTER 2: Incidence and Metric Geometry
- 2.1 Definition and Models of Incidence Geometry
- 2.2 Metric Geometry
- 2.3 Special Coordinate Systems
- CHAPTER 3: Betweenness and Elementary Figures
- 3.1 An Alternative Description of the Cartesian Plane
- 3.2 Betweenness
- 3.3 Line Segments and Rays
- 3.4 Angles and Triangles
- CHAPTER 4: Plane Separation
- 4.1 The Plane Separation Axiom
- 4.2 PSA for the Euclidean and Poincaré Planes
- 4.3 Pasch Geometries
- 4.4 Interiors and the Crossbar Theorem
- 4.5 Convex Quadrilaterals
- CHAPTER 5: Angle Measure
- 5.1 The Measure of an Angle
- 5.2 The Moulton Plane
- 5.3 Perpendicularity and Angle Congruence
- 5.4 Euclidean and Poincaré Angle Measure (optional)
- CHAPTER 6: Neutral Geometry
- 6.1 The Side-Angle-Side Axiom
- 6.2 Basic Triangle Congruence Theorems
- 6.3 The Exterior Angle Theorem and Its Consequences
- 6.4 Right Triangles
- 6.5 Circles and Their Tangent Lines
- 6.6 The Two Circle Theorem (optional)
- 6.7 The Synthetic Approach
- CHAPTER 7: The Theory of Parallels
- 7.1 The Existence of Parallel Lines
- 7.2 Saccheri Quadrilaterals
- 7.3 The Critical Function
- CHAPTER 8: Hyperbolic Geometry
- 8.1 Asymptotic Rays and Triangles
- 8.2 Angle Sum and the Defect of a Triangle
- 8.3 The Distance Between Parallel Lines
- CHAPTER 9: Euclidean Geometry
- 9.1 Equivalent Forms of EPP
- 9.2 Similarity Theory
- 9.3 Some Classical Theorems of Euclidean Geometry
- CHAPTER 10: Area
- 10.1 The Area Function
- 10.2 The Existence of Euclidean Area
- 10.3 The Existence of Hyperbolic Area
- 10.4 Bolyai's Theorem
- CHAPTER 11: The Theory of Isometries
- 11.1 Collineations and Isometries
- 11.2 The Klein and Poincaré Disk Models (optional)
- 11.3 Reflections and the Mirror Axiom
- 11.4 Pencils and Cycles
- 11.5 Double Reflections and Their Invariant Sets
- 11.6 The Classification of Isometries
- 11.7 The Isometry Group
- 11.8 The SAS Axiom in $\mathscr H$
- 11.9 The Isometry Groups of $\mathscr E$ and $\mathscr H$
- Bibliography
- Index
Source work progress
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