A Gateway to Modern Geometry: The Poincare

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 the 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.

Euclidean Geometry	p. 1
Euclidean Rigid Motions	p. 25
Inversions	p. 41
The Hyperbolic Plane	p. 53
Euclidean Versus Hyperbolic Geometry	p. 67
The Angles of the Hyperbolic Triangle	p. 79
Hyperbolic Area	p. 89
The Trigonometry of the Hyperbolic Triangle	p. 99
Complex Numbers and Rigid Motions	p. 109
Absolute Geometry and the Angles of the Triangle	p. 137
Spherical Trigonometry and Elliptic Geometry	p. 143
Differential Geometry and Gaussian Curvature	p. 157
The Cross-Ratio and the Unit Disk Model	p. 173
The Beltrami-Klein Model	p. 199
A Brief History of Non-Euclidean Geometry	p. 211
Spheres and Horospheres	p. 219
Proofs of Some of Euclid's Propositions	p. 235
Formulas for Hyperbolic Trigonometric Functions	p. 249
Sources, References and Suggested Readings	p. 251
Index	p. 253
Table of Contents provided by Blackwell. All Rights Reserved.

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A Gateway to Modern Geometry: The Poincare Half-Plane

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