Editorial Reviews
Product Description
The study of the 3 conics : ellipses, hyperbolas and parabolas is a fascinating topic of analytic geometry. This book breaks a long tradition practiced in most classical math text books in which the conics discussed are confined to a single axis-aligned orientation and a single reference point, the origin. Using a Computer Algebraic System, Maple , complete sets of formulas are developed for conics with arbitrary alignment and positioning. The treatment of the conics proceeds in a logical fashion from the derivation of the 7 position independent parameters, followed by the generation of up to 36 positional parameters, and finally to the computation of the A..F coefficients of the conic polynomials. Fundamental and compound transformations of the conics are described and relevant formulas are generated using surprisingly simple techniques. Two extensions go beyond the basic conics treatment. First, tangent conditions between lines and conics and between two conics are stated and computed enabling the generation of a rich set of corresponding formulas. Now, inscribing conics of any alignment or position into triangles and quadrilaterals becomes possible. Second, a set of 54 parameters of conics placed in the 3-D coordinate system are generated, and the 3-D display of the corresponding conics is described step-by-step. Over 50 challenging examples are provided with detailed explanations and illustrations. These examples include positioning, orientation, sizing, shaping, transformation, parameterization of the conic, and the construction of conics subject to various tangent and proximity constraints. In addition conics through 3, 4 and 5 points are demonstrated. An invaluable resource to the practitioner, the TOOLBOX, spans over 100 pages and contains hundreds of well organized formulas generated and used throughout the main text. All formulas and their generating algorithms are available in electronic form upon request.
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