A Mathematical Space Odyssey: Solid Geometry In The 21st Century
A Mathematical Space Odyssey: Solid Geometry in the 21st Century
Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. This book presents techniques for proving a variety of geometric results in three dimensions. Special attention is given to prisms, pyramids, platonic solids, cones, cylinders and spheres, as well as many new and classical results. A chapter is devoted to each of the following basic techniques for exploring space and proving theorems: enumeration, representation, dissection, plane sections, intersection, iteration, motion, projection, and folding and unfolding. The book includes a selection of Challenges for each chapter with solutions, references and a complete index. The text is aimed at secondary school and college and university teachers as an introduction to solid geometry, as a supplement in problem solving sessions, as enrichment material in a course on proofs and mathematical reasoning, or in a mathematics course for liberal arts students.
My preference for "keeping things planar" has persisted to this day, and affects the way I do certain things. For the last several years, for example, I have taught a two-semester course at the senior undergraduate level in geometry, and although in...