Analytical Quadrics

Barry Spain, I. N. Sneddon, S. Ulam, M. Stark

• Publisher: Pergamon
• Year: 2014
• Print ISBN: 9780080136264
• eBook ISBN: 9781483138299
• Topic: Mathematics
• Subtopic: Geometry
• Index: Mathematics

Analytical Quadrics focuses on the analytical geometry of three dimensions. The book first discusses the theory of the plane, sphere, cone, cylinder, straight line, and central quadrics in their standard forms. The idea of the plane at infinity is introduced through the homogenous Cartesian coordinates and applied to the nature of the intersection of three planes and to the circular sections of quadrics. The text also focuses on paraboloid, including polar properties, center of a section, axes of plane section, and generators of hyperbolic paraboloid. The book also touches on homogenous coordinates. Concerns include intersection of three planes; circular sections of central quadric; straight line; and circle at infinity. The book also discusses general quadric and classification and reduction of quadric. Discussions also focus on linear systems of quadrics and plane-coordinates. The text is a valuable reference for readers interested in the analytical geometry of three dimensions.

Table of contents

• Front Cover
• Analytical Quadrics
• Copyright Page
• Table of Contents
• PREFACE
• CHAPTER I. INTRODUCTION
• CHAPTER II. PLANE—STRAIGHT LINE
• CHAPTER III. SPHERE
• CHAPTER IV. QUADRIC CONE—CYLINDER
• CHAPTER V. CENTRAL QUADRIC
• CHAPTER VI. PARABOLOID
• CHAPTER VII. HOMOGENEOUS COORDINATES
• CHAPTER VIII. GENERAL QUADRIC
• CHAPTER IX. TRANSFORMATION OF AXES—INVARIANTS
• CHAPTER X. CLASSIFICATION AND REDUCTION OF QUADRIC
• CHAPTER XI. FOCI—CONFOCALS
• CHAPTER XII. LINEAR SYSTEMS OF QUADRICS
• CHAPTER XIII. PLANE-COORDINATES
• APPENDICES
• INDEX