The Poincare Half-Plane: A Gateway to Modern Geometry / Edition 1

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Editorial Reviews

In the 1880s, over fifty years after the discovery of the hyperbolic plane, Poincare pointed out that this plane provides a very useful context for describing the properties of the solutions of an important class of differential equations. Topics include Euclidean rigid motions, inversions, Euclidean versus hyperbolic geometry, hyperbolic area, complex numbers and rigid motions, spherical trigonometry and elliptic geometry, differential geometry and Gaussian curvature, and the Beltrami-Klein model. Many exercises follow each chapter. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780867202984
  • Publisher: Jones & Barlett Learning
  • Publication date: 4/9/1993
  • Series: Math Series
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 312
  • Product dimensions: 6.00 (w) x 9.30 (h) x 0.90 (d)

Table of Contents

Chapter Dependencies
Ch. 1 Euclidean Geometry 1
Ch. 2 Euclidean Rigid Motions 35
Ch. 3 Inversions 51
Ch. 4 The Hyperbolic Plane 63
Ch. 5 Euclidean Versus Hyperbolic Geometry 79
Ch. 6 The Angles of the Hyperbolic Triangle 93
Ch. 7 Hyperbolic Area 109
Ch. 8 The Trigonometry of the Hyperbolic Triangle 119
Ch. 9 Complex Numbers and Rigid Motions 131
Ch. 10 Absolute Geometry and the Angles of the Triangle 161
Ch. 11 Spherical Trigonometry and Elliptic Geometry 167
Ch. 12 Differential Geometry and Gaussian Curvature 183
Ch. 13 The Cross Ratio and the Unit Disk Model 207
Ch. 14 The Beltrami-Klein Model 233
Ch. 15 A Brief History of Non-Euclidean Geometry 247
Ch. 16 Spheres and Horospheres 257
Appendix 277
Bibliography 293
Index 295
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  • Anonymous

    Posted May 6, 2005

    Excellent book

    I bought this book while visiting Stanford University. I heard about non-euclidian geometries but never had really seen what it is. This book explains the basics, limiting itself to dimension 2. This clearly is an excellent idea. The reader can easily see the reasons why such or such definition was considered. This is a very good step to go further and provides motivation for it. Moreover, Mr Stahl is very kind to answer the questions he is asked. This is sufficiently rare to be noticed and encouraged!

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