Book:Richard S. Millman/Geometry: A Metric Approach with Models/Second Edition

Part of the Undergraduate Texts in Mathematics series.

Subject Matter

 * Geometry

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