Geometry of Curves and Surfaces with MAPLE, Softcover reprint of the original 1st ed. 2000

This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource or self-study reference. With over 100 stimulating exercises, problems and solutions, {\it Geometry of Curves and Surfaces with Maple} will integrate traditional differential and non- Euclidean geometries with more current computer algebra systems in a practical and user-friendly format.

MAPLE V: A Quick Reference.- I Functions and Graphs with MAPLE.- 1 Graphs of Tabular and Continuous Functions.- 2 Graphs of Composed Functions.- 3 Interpolation of Functions.- 4 Approximation of Functions.- II Curves with MAPLE.- 5 Plane Curves in Rectangular Coordinates.- 6 Curves in Polar Coordinates.- 7 Asymptotes of Curves.- 8 Space Curves.- 9 Tangent Lines to a Curve.- 10 Singular Points on Curves.- 11 Length and Center of Mass of a Curve.- 12 Curvature and Torsion of Curves.- 13 Fractal Curves and Dimension.- 14 Spline Curves.- 15 Non-Euclidean Geometry in the Half-Plane.- 16 Convex Hulls.- III Polyhedra with MAPLE.- 17 Regular Polyhedra.- 18 Semi-Regular Polyhedra.- IV Surfaces with MAPLE.- 19 Surfaces in Space.- 20 Some Classes of Surfaces.- 21 Some Other Classes of Surfaces.- References.