A Treatise on the Differential Geometry of Curves and Surfaces (Classic Reprint) - Softcover

Beecher, Henry Ward

Softcover

ISBN 10: 1451004672 ISBN 13: 9781451004670

Publisher: Forgotten Books, 2012

Synopsis

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 Frenet-S erret formulas. In this way the student is made familiar with a method which is similar to that used by Darboux in the first volume of his Lemons, and to that of Cesaro in his Geometria I ntrinseca. This method is not only of great advantage in the treat ment of certain topics and in the solution of problems, but it is valuable in developing geometrical thinking. The remainder of the book may be divided into three parts. The first, consisting of Chapters II-YI, 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 properties of a surface are derived from the discussion of two quadratic differential forms. However, little or no space is given to the algebraic treatment of differential forms and their invariants. In addition, the method of moving axes, as defined in the first chapter, has been extended so as to be applicable to an investigation of the properties of surfaces and groups of surfaces. The extent of the theory concerning ordinary points is so great that no attempt has been made to consider the exceptional problems. For a discussion of such questions as the existence of integrals of diff
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About this edition

• Publisher: Forgotten Books
• Publication date: 2012
• ISBN 10: 1451004672
• ISBN 13: 9781451004670
• Binding: Paperback
• Number of pages: 488