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Excerpt from Lectures on the Differential Geometry of Curves and Surfaces
The book concludes with a single chapter that contains an introduction to the elementary theory of congruences of curves.
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Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Excerpt from Lectures on the Differential Geometry of Curves and Surfaces
In the second section, consisting of chapters II - VI, the subject-matter is the properties of curves upon any general surface in space. Some classes of these curves (e.g. lines of curvature) are organically connected with the surface; they are completely determined by the elements of the surface to which they belong. Other curves, such as geodesics, have an equally organic relation with the surface; but they are not determined solely by the elements of the surface, for they can satisfy some arbitrarily assigned condition or conditions. Again, quite arbitrary curves and families of curves can be assumed upon a surface; not a little attention has been devoted to methods for constructing differential invariants which, being in value independent of parameters of reference, express the geometrical magnitudes of the curves, subject, of course, to the dominance of the intrinsic magnitudes of the surface containing the curve or curves.
In the third section, consisting of chapters VII - XI, the subject-matter is surfaces in general, rather than particular configurations on surfaces. The most ordinary methods of point-to-point correspondence and comparison of surfaces are explained. Surfaces, which are defined (wholly or partially) by intrinsic properties, are considered, special attention being paid to minimal surfaces. Families of surfaces are discussed, according to the respective definitions that ultimately establish the families; the most obvious instance relates to those surfaces which have plane or spherical sets of lines of curvature. Lastly, a brief sketch of the simplest fundamental properties of triply orthogonal systems is given.
The book concludes with a single chapter that contains an introduction to the elementary theory of congruences of curves, specially of straight lines and of circles.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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- EditorialForgotten Books
- Año de publicación2018
- ISBN 10 1330115457
- ISBN 13 9781330115459
- EncuadernaciónTapa blanda
- IdiomaInglés
- Número de páginas560
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Lectures on the Differential Geometry of Curves and Surfaces (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book delves into the intricate world of differential geometry, specifically focusing on the properties of curves and surfaces in three-dimensional Euclidean space. It presents a comprehensive exploration of fundamental concepts, including tangents, normals, curvature, and torsion of curves, as well as the geometric characteristics of surfaces such as lines of curvature, geodesics, and minimal surfaces. Grounded in classical mathematical analysis, the author guides readers through the intricacies of these geometric entities. The book offers a rigorous yet accessible treatment of the subject, drawing upon the works of renowned mathematicians like Gauss and Darboux. It covers a wide range of topics, from the basic properties of skew curves to the advanced theory of congruences and triply orthogonal systems. The book's thematic depth lies in its exploration of the interplay between curves and surfaces, highlighting the organic connections and differential invariants that govern their relationships. It delves into the intrinsic properties of these geometric objects, independent of their specific positions or orientations in space. Through its insightful analysis, this book reveals the profound elegance and underlying unity within the realm of differential geometry, demonstrating how seemingly disparate geometric concepts are intricately interwoven and governed by fundamental mathematical principles. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781330115459_0
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Lectures on the Differential Geometry of Curves and Surfaces Classic Reprint
Librería: PBShop.store US, Wood Dale, IL, Estados Unidos de America
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330115459
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Lectures on the Differential Geometry of Curves and Surfaces Classic Reprint
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330115459
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