
History of Mathematics 1996; 153 pp; softcover Volume: 10 Reprint/Revision History: reprinted 1998 ISBN10: 0821809229 ISBN13: 9780821809228 List Price: US$50 Member Price: US$40 Order Code: HMATH/10.S See also: Papers on Topology: Analysis Situs and Its Five Supplements  Henri Poincare Lectures on Number Theory  P G L Dirichlet (with supplements by R Dedekind)  This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré 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 overduenot 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 Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in lowdimensional 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'seye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Poincaré in their full brilliance. Cover picture reproduced with permission of Dr. Konrad Polthier. Readership Graduate students and research mathematicians specializing in geometry. Reviews "Translations are well done and very readable ... papers ... are well chosen ... an extremely attractive and valuable book to have and to read ... fills an important niche in the mathematical literature by making these papers available to a contemporary audience ... allows the modern reader to see how the great mathematicians of another time viewed both their subject and mathematics in general, a view which can still be inspirational."  Bulletin of the London Mathematical Society Table of Contents



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