Softcover ISBN:  9780821809228 
Product Code:  HMATH/10.S 
List Price:  $53.00 
MAA Member Price:  $47.70 
AMS Member Price:  $42.40 
Electronic ISBN:  9781470438784 
Product Code:  HMATH/10.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 

Book DetailsHistory of MathematicsVolume: 10; 1996; 153 ppMSC: Primary 51; Secondary 01; 53; 30;
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 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 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.ReadershipGraduate students and research mathematicians specializing in geometry.

Table of Contents

Chapters

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 socalled noneuclidean geometry)

On the socalled 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


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


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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 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 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.
Graduate students and research mathematicians specializing in geometry.

Chapters

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 socalled noneuclidean geometry)

On the socalled 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

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