A Treatise on the Differential Geometry of Curves and Surfaces (1909)
Luther Pfahler Eisenhart
ISBN: | 9781169975927 |
Publisher: | Literary Licensing, LLC |
Published: | 7 August, 2014 |
Format: | Paperback |
Editions: |
4 other editions
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A Treatise on the Differential Geometry of Curves and Surfaces (1909)
Luther Pfahler Eisenhart
A TREATISE ON THE DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES BY IJTTHEU PFAIILKR EISENHAIIT PKOPKHHOIt OK MATUKMATKH IN 1 ltINCMTON UNIVJCIWITY GOT AND COMPANY BOSTON NEW YOKE CHICAGO LONDON PREFACE This book is a development from courses which I have given in Princeton for a number of years. During this time I have come to feel that more would be accomplished by my students if they had an introductory treatise written in English and otherwise adapted to the use of men beginning their graduate work. Chapter I is devoted to the theory of twisted curves, the method in general being that which is usually followed in discussions of this subject. But in addition I have introduced the idea of moving axes, and have derived the formulas pertaining thereto from the previously obtained Freiiet-Serret fornmlas. In this way the student is made familiar with a method which is similar to that used by Darboux in the tirst volume of his Lepons, and to that of Cesaro in his Gcomctria Ittiriiiseca. This method is not only of great advantage in the treat ment of certain topics and in the solution of problems, but it is valu able iu developing geometrical thinking. The remainder of the book may be divided into threo parts. The iirst, consisting of Chapters II-VI, deals with the geometry of a sur face in the neighborhood of a point and the developments therefrom, such as curves and systems of curves defined by differential equa tions. To a large extent the method is that of Gauss, by which the
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