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.

• Promotes the beauty and importance of a subject that has largely disappeared from the curriculum
• Includes many impressive figures that illustrate the main results and a selection of pictures of 3D works of art to enrich the text
• Each chapter includes a selection of Challenges, with solutions at the end of the book, for the reader to explore further properties and applications