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

From ProofWiki
Jump to navigation Jump to search

Richard S. Millman and George D. Parker: Geometry: A Metric Approach with Models (2nd Edition)

Published $1991$, 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