Sources of Hyperbolic Geometry

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American Mathematical Soc., 1996 - Mathematics - 153 pages
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This book presents, for the first time 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 Lobachevsky seems long 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. The unified setting and historical context reveal the insights of Beltrami, Klein, and Poincare in their full brilliance.

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Introduction to Beltramis
Introduction to Beltramis
Introduction to Kleins
Introduction to Poincares
Translation of Poincares

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Hyperbolic Geometry
James Anderson
Limited preview - 2005
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About the author (1996)

John Stillwell is professor of mathematics at the University of San Francisco. His many books include "Mathematics and Its History" and "Roads to Infinity".

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