Revised edition of: Poincaré́́ half-plane. Boston : Jones and Bartlett Publishers, c1993.
Includes bibliographical references (pages 251-252) and index.
Euclidean geometry -- Euclidean rigid motions -- Inversions -- Hyperbolic plane -- Euclidean versus hyperbolic geometry -- Angles of the hyperbolic triangle -- Hyperbolic area -- Trigonometry of the hyperbolic triangle -- Complex numbers and rigid motions -- Absolute geometry and the angles of the triangle -- Spherical trigonometry and elliptic geometry -- Differential geometry and gaussian curvature -- Cross-ratio and the unit disk model -- Beltrami-Klein model -- Brief history of non-Euclidean geometry -- Spheres and horospheres -- Appendix A : Proofs of some of Euclid's propositions -- Appendix B : Formulas for hyperbolic trigonometric functions.