Analytic Geometry of Space (Classic Reprint) - Couverture souple

Gaebelein, Arno C.

9781440091773: Analytic Geometry of Space (Classic Reprint)

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ISBN 10 : 1440091773 ISBN 13 : 9781440091773

Editeur : Forgotten Books, 2018

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Analytic Geometry of Space by Virgil Snyder offers a rigorous, coordinate-based study of three-dimensional geometry, extending the ideas of plane analytic geometry into space.

This edition presents the foundations of coordinates, planes, lines, and quadric surfaces with clear, structured explanations. The book frames space with three mutually perpendicular coordinate planes, defines axes and coordinates, and builds up to complex objects like spheres and quadric surfaces. It covers transformations, projections, and practical methods for describing space using algebraic equations, making it a comprehensive reference for advanced geometry study.

Clear introduction to rectangular coordinates and space coordinates
Equations and properties of planes, lines, and quadric surfaces
Methods for transforming space and understanding projections
Problem sets and exercises to reinforce concepts

Ideal for readers of advanced geometry and students seeking a thorough, math-driven treatment of space.

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Pr�sentation de l'�diteur

In this book, which is planned for an introductory course, the first eight chapters include the subjects usually treated in rectangular coordinates. They presuppose as much knowledge of algebra, geometry, and trigonometry as is contained in the major requirement of the College Entrance Examination Board, and as much plane analytic geometry as is contained in the better elementary textbooks. In this portion, proofs of theorems from more advanced subjects in algebra are supplied as needed. A mong the features of this part are the development of linear systems of planes, plane coordinates, the concept of infinity, the treatment of imaginaries, and the distinction between centers and vertices of quadric surfaces. The study of this portion can be regarded as a first course, not demanding more than thirty or forty lessons. In Chapter IX tetrahedral coordinates are introduced by means of linear transformations, under which various invariant properties are established. These coordinates are used throughout the next three chapters. The notation is so chosen that no ambiguity can arise between tetrahedral and rectangular systems. The selection of subject matter is such as to be of greatest service for further study of algebraic geometry. In Chapter XIII a more advanced knowledge of plane analytic geometry is presupposed, but the part involving Pliicker snumbers may be omitted without disturbing the continuity of the subject. In the last chapter extensive use is made of the calculus, including the use of partial differentiation and of the element of arc. The second part will require about fifty lessons.
(Typographical errors above are due to OCR software and don't occur in the book.)

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Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.

Forgotten Books' Classic Reprint Series utilizes the l

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�diteur: Forgotten Books
Date d'�dition: 2018
Langue: anglais
ISBN 10: 1440091773
ISBN 13: 9781440091773
Reliure: Broch�
Nombre de pages: 308
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Analytic Geometry of Space (Classic Reprint)

Virgil Snyder

Edit� par Forgotten Books, 2018

ISBN 10 : 1440091773 ISBN 13 : 9781440091773

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Vendeur : Forgotten Books, London, Royaume-Uni

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Paperback. Etat : New. Print on Demand. This book offers a comprehensive exploration of the geometry of three-dimensional space, a field that has fascinated mathematicians for centuries. Building upon the foundations of plane analytic geometry, the author guides readers through a detailed examination of planes, lines, and quadric surfaces. The book employs various coordinate systems â� � including rectangular, polar, cylindrical, and spherical â� � to provide a multifaceted understanding of spatial relationships. The text delves into the complex relationship between equations and geometric figures, offering readers a powerful tool for visualizing and analyzing three-dimensional objects. Through the exploration of diverse forms of quadric surfaces, including ellipsoids, hyperboloids, paraboloids, and cones, the author reveals the underlying patterns and principles that govern spatial geometry. The bookâ� �s exploration of linear transformations and invariant properties offers a deeper understanding of the fundamental nature of geometric objects. The use of tetrahedral coordinates, introduced through linear transformations, provides a unique and elegant framework for studying quadric surfaces and their properties. Ultimately, this book serves as a valuable resource for those seeking to unravel the complexities of spatial geometry. 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. N� de r�f. du vendeur 9781440091773_0

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