This is a revised and updated edition of Graham Nerlich's classic book (1976). It develops a metaphysical account of space that treats it as a real and concrete entity, showing that shape plays a key explanatory role in space and spacetime theories. Arguing that geometrical explanation is very like
The Shape of Space
โ Scribed by Jeffrey R. Weeks
- Publisher
- Chapman and Hall/CRC
- Year
- 2019
- Tongue
- English
- Leaves
- 365
- Series
- Textbooks in Mathematics
- Edition
- 3
- Category
- Library
No coin nor oath required. For personal study only.
โฆ Synopsis
The Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spacesโstretching studentsโ minds as they learn to visualize new possibilities for the shape of our universe.
Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space.
Features of the Third Edition:
- Full-color figures throughout
- "Picture proofs" have replaced algebraic proofs
- Simpler handles-and-crosscaps approach to surfaces
- Updated discussion of cosmological applications
- Intuitive examples missing from many college and graduate school curricula
About the Author:
Jeffrey R. Weeks is a freelance geometer living in Canton, New York. With support from the U.S. National Science Foundation, the MacArthur Foundation and several science museums, his work spans pure mathematics, applications in cosmology andโclosest to his heartโexposition for the general public.
โฆ Table of Contents
Contents
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
PART I Surfaces and Three-Manifolds
1. Flatland
2. Gluing
3. Vocabulary
4. Orientability
5. Classification of Surfaces
6. Products
7. Flat Manifolds
8. Orientability vs. Two-Sidedness
PART II Geometries on Surfaces
9. The Sphere
10. The Hyperbolic Plane
11. Geometries on Surfaces
12. The Gauss-Bonnet Formula and the Euler Number
PART III Geometries on Three-Manifolds
13. Four-Dimensional Space
14. The Hypersphere
15. Hyperbolic Space
16. Geometries on Three-Manifolds I
17. Bundles
18. Geometries on Three-Manifolds II
PART IV The Universe
19. The Universe
20. The History of Space
Appendix A Answers
Appendix B Bibliography
Appendix C Conwayโs ZIP Proof
Index
๐ SIMILAR VOLUMES
This is a revised and updated edition of Graham Nerlich's classic book (1976). It develops a metaphysical account of space that treats it as a real and concrete entity, showing that shape plays a key explanatory role in space and spacetime theories. Arguing that geometrical explanation is very like
This is a revised and updated edition of Graham Nerlich's classic book (1976). It develops a metaphysical account of space that treats it as a real and concrete entity, showing that shape plays a key explanatory role in space and spacetime theories. Arguing that geometrical explanation is very like
<p></p> <p>The Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spacesโstretching studentsโ minds as they learn to visualize new possibilities for the shape