Geometry: A Metric Approach with Models

R S Millman,G D Parker

Format
Paperback
Publisher
Springer
Country
Published
24 January 2012
Pages
372
ISBN
9781468401325

Geometry: A Metric Approach with Models

R S Millman,G D Parker

This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

1 Preliminary Notions.- 1.1 Axioms and Models.- 1.2 Sets and Equivalence Relations.- 1.3 Functions.- 2 Incidence and Metric Geometry.- 2.1 Definition and Models of Incidence Geometry.- 2.2 Metric Geometry.- 2.3 Special Coordinate Systems.- 3 Betweenness and Elementary Figures.- 3.1 An Alternative Description of the Euclidean Plane.- 3.2 Betweenness.- 3.3 Line Segments and Rays.- 3.4 Angles and Triangles.- 4 Plane Separation.- 4.1 The Plane Separation Axiom.- 4.2 PSA for the Euclidean and Hyperbolic Planes.- 4.3 Pasch Geometries.- 4.4 Interiors and the Crossbar Theorem.- 4.5 Convex Quadrilaterals.- 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 Hyperbolic Angle Measure (optional).- 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 (optional).- 7 The Theory of Parallels.- 7.1 The Existence of Parallel Lines.- 7.2 Saccheri Quadrilaterals.- 7.3 The Critical Function.- 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.- 9 Euclidean Geometry.- 9.1 Equivalent Forms of EPP.- 9.2 Similarity Theory.- 9.3 Some Classical Theorems of Euclidean Geometry.- 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.- 11 The Theory of Isometries.- 11.1 Collineations and Isometries.- 11.2 The Klein and Poincare 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 ?.- 11.9 The Isometry Groups of ? and ?.

This item is not currently in-stock. It can be ordered online and is expected to ship in 7-14 days

Our stock data is updated periodically, and availability may change throughout the day for in-demand items. Please call the relevant shop for the most current stock information. Prices are subject to change without notice.

Sign in or become a Readings Member to add this title to a wishlist.