منابع هندسه هایپرولیک (تاریخ ریاضیات)

This text presents, in English, the papers of Beltrami, Klein and Poincare that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Labachevsky seems overdue - not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincare brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. Cover Title page Preface Contents Translator’s introduction (Essay on the interpretation of noneuclidean geometry) Essay on the interpretation of noneuclidean geometry Translator’s introduction (Fundamental theory of spaces of constant curvature) Fundamental theory of spaces of constant curvature Translator’s introduction (On the so-called noneuclidean geometry) On the so-called noneuclidean geometry Translator’s introduction (Theory of Fuchsian groups/Memoir on Kleinian groups/On the applications of noneuclidean geometry to the theory of quadratic Theory of Fuchsian groups/Memoir on Kleinian groups/On the applications of noneuclidean geometry to the theory of quadratic forms Index Back Cover Consists Of Papers By Eugenio Beltrami, Felix Klein And Jules Henri Poincaré, With Introductions By Stillwell. John Stillwell. Includes Bibliographical References And Index.