A Mathematical Space Odyssey

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.

Contents; Preface; 1. Introduction; 2. Enumeration; 3. Representation; 4. Dissection; 5. Plane sections; 6. Intersection; 7. Iteration; 8. Motion; 9. Projection; 10. Folding and unfolding; Solutions to the challenges; References; Index; About the authors.