A Gateway to Modern Geometry: The Poincare Half-Plane: The Poincare Half-Plane

by Saul Stahl

Overview

Stahl's Second Edition continues to provide students with the elementary and constructive development of modern geometry that brings them closer to current geometric research. At the same time, repeated use is made of high school geometry, algebra, trigonometry, and calculus, thus reinforcing students' understanding of these disciplines as well as enhancing their perception of mathematics as a unified endeavor. This distinct approach makes these advanced geometry principles accessible to undergraduates and graduates alike. © 2008 | 256 pages

Product Details

ISBN-13:	9780763753818
Publisher:	Jones & Bartlett Learning
Publication date:	12/11/2007
Edition description:	2E
Pages:	256
Product dimensions:	7.40(w) x 9.20(h) x 1.00(d)

About the Author

Dr. Stahl's research area is graph theory and his mathematical avocation is the evolution of mathematical ideas. He has published several textbooks in geometry, algebra, analysis and game theory. In all of these books the histrory of the subject is an integral part of the development of the subject matter. He has three children and his hobbies are dance and languages.

Table of Contents

Chapter Preface
Chapter 1 Euclidean Geometry
Chapter 2 Euclidean Rigid Motions
Chapter 3 Inversions
Chapter 4 The Hyperbolic Plane
Chapter 5 Euclidean Versus Hyperbolic Triangle
Chapter 6 The Angles of the Hyperbolic Triangle
Chapter 7 Hyperbolic Area
Chapter 8 The Trigonometry of the Hyperbolic Triangle
Chapter 9 Complex Numbers and Rigid Motions
Chapter 10 Absolute Geometry and the Angles of the Triangle
Chapter 11 Spherical Trigonometry and Elliptic Geometry
Chapter 12 Differential Geometry and Gaussian Curvature
Chapter 13 The Cross-Ration and the Unit Disk Model
Chapter 14 The Beltrami-Klein Model
Chapter 15 A Brief History of Non-Euclidean Geometry
Chapter 16 Spheres and Horospheres
Chapter Appendix A Proofs of Some of Euclid's Propositions
Chapter Appendix B Formulas for Hyperbolic Trigonometric Functions
Chapter Sources, References and Suggested Readings
Chapter Index