Exploring Quadric Surfaces with Maple

This paper explores some of the basic and most interesting facts about quadric surfaces. It describes the canonical coordinate transformations required to eliminate cross terms from the equation of a general quadric equation. It explains how to use these coordinates to obtain each of the seventeen canonical quadrics. It further describes the determination of the physical axis and angle of rotation. It describes the salient feature of a Maple 11 worksheet that can be used to analyze general quadric surfaces. This paper has several objectives. It provides instructors with a convenient technology based approach to introduce quadrics and rotations to their classes using the worksheet. At the same time, it allows us to consider several interesting mathematical topics relevant to quadric surfaces. Finally, it demonstrates that the symbolic, numerical, and graphical capabilities of a Computer Algebra System such as Maple 11 can be used to investigate a very complex problem in a general way to obtain important insights. Rotations of Quadric Surfaces