Projective Differential Geometry Of Curves And Ruled Surfaces (1906) - Tapa dura

Wilczynski, Ernest Julius

 
9781436645300: Projective Differential Geometry Of Curves And Ruled Surfaces (1906)
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ISBN 10: 1436645301 ISBN 13: 9781436645300
Editorial: Kessinger Publishing, 2008

Sinopsis

Projective Differential Geometry of Curves and Ruled Surfaces is a comprehensive mathematical treatise written by Ernest Julius Wilczynski and originally published in 1906. The book focuses on projective differential geometry, a branch of mathematics concerned with the properties of curves and surfaces under projective transformations, and is intended for advanced students and researchers in the field.The book is divided into three main parts. The first part provides an introduction to the basic concepts of projective geometry, including projective transformations, projective coordinates, and cross ratios. The second part focuses on the differential geometry of curves, including the theory of curvature and torsion, the Frenet-Serret formulas, and the classification of curves according to their properties. The third part is devoted to the differential geometry of ruled surfaces, including the theory of developable surfaces, the geometry of the tangent plane, and the classification of surfaces according to their properties.Throughout the book, Wilczynski provides a rigorous and detailed treatment of the subject matter, with numerous examples, exercises, and proofs. The book also includes a comprehensive bibliography and index, making it a valuable resource for anyone interested in the study of projective differential geometry.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

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Reseña del editor

This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

Reseña del editor

In the geometrical investigations of the last century, one of the most fundamental distinctions has been that between metrical and projective geometry. It is a curious fact that this classification seems to have given rise to another distinction, which is not at all justiiied by the nature of things. There are certain properties of curves, surfaces, etc., which may be deduced for the most general configurations of their kind, depending only upon the knowledge that certain conditions of continuity are fulfilled in the vicinity of a certain point. These are the so-called infinitesimal properties and are naturally treated by the methods of the differential calculus. The curious fact to which we have referred is that, but for rare exceptions, these infinitesimal properties have been dealt with only from the metrical point of view. Projective geometry, which has made such progress in the course of the century, has apparently disdained to consider the infinitely small parts into which its configurations may be decomposed. It has gained the possibility of making assertions about its contigmations as a whole, only by limiting its field to the consideration of algebraic cases, a restriction which is unnecessary in differential geometry. Between the metrical differential geometry of Monge and Gauss, and the algebraic projective geometry of Poncelet and Pliicker, there is left, therefore, the field of projective differential geometry whose nature partakes somewhat of both. The theorems of this kind of geometry are concerned with projective properties of the ininitesimal elements. As in the ordinary differential geometry, the process of integration may lead to statements concerning properties of the configuration as a whole. But, of course, such integration is possible only in special cases. Even with this limitation, however, which lies in the nature of things, the fie
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Editorial
Kessinger Publishing
Año de publicación
2008
Idioma
Inglés
ISBN 10 
1436645301
ISBN 13 
9781436645300
Encuadernación
Tapa dura
Número de páginas
308
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9780548861110: Projective Differential Geometry Of Curves And Ruled Surfaces (1906)

Edición Destacada

ISBN 10:  0548861110 ISBN 13:  9780548861110
Editorial: Kessinger Publishing, LLC, 2008
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