Sources of Hyperbolic Geometry: No. 10 (History of Mathematics) - Hardcover

Hardcover

ISBN 10: 0821805290 ISBN 13: 9780821805299

Publisher: American Mathematical Society, 1996

Synopsis

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 Labachevsky 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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1996
• Language: English
• ISBN 10: 0821805290
• ISBN 13: 9780821805299
• Binding: Hardcover
• Number of pages: 153
• Editor: Stillwell John