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.
Rezensionen / Stimmen
If I had had access to this text in my formative years, my entire attitude about multidimensional geometry might well be different now... The writing seemed to me to be clear, though succinct and efficient. The authors have managed to keep the prerequisites for reading this book to a minimum; certainly a year of calculus is sufficient for just about everything done here, and even a college freshman without any calculus would find almost all of the text comprehensible, since calculus is used in only a handful of circumstances. The book employs a number of nice pedagogical features... It's certainly something that anybody interested in geometry would want to take a look at - even if, like me, you didn't think you were all that interested in solid geometry." - Mark Hunacek, MAA Reviews
"This book provides a valuable resource for the study of solid geometry that could be used by teachers all the way from late elementary school through college." - Charles Ashbacher
"A Mathematical Space Odyssey is an excellent and thorough introduction to the basic ideas of solid geometry... The liberal use of diagrams and figures provides good support for the mathematics presented. The book is written in such a way that it is suitable for anyone with an understanding of basic algebra, with plenty of figures to support the mathematics presented... It would be an excellent textbook for an introductory college course in solid geometry." - Hilary Smith Risser, Mathematics Teacher
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Maße
Höhe: 211 mm
Breite: 142 mm
Dicke: 21 mm
Gewicht
ISBN-13
978-0-88385-358-0 (9780883853580)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Roger B. Nelsen, Professor Emeritus of Mathematics, Lewis & Clark College, USA.
Claudi Alsina, Professor of Mathematics, Polytechnic University of Catalonia, Spain.
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
