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The shape of space / Jeffrey R. Weeks

Weeks, Jeffrey R.
Material type: materialTypeLabelBook; Format: print Series: Monographs and textbooks in pure and applied mathematics ; 249.Publisher: New York : Marcel Dekker, 2002Edition: 2nd ed.Description: XII, 382 p. ; 23 cm.ISBN: 0-8247-0709-5; 9780824707095.Subject(s): Topología | Cristalografía
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515.12/WEE/sha (Browse shelf)   Shelving location | Bibliomaps® BIBLIOG. RECOM. 3744398426


515.12/WEE/sha (Browse shelf) Checked out PREST. LIBROS 31/01/2019 3741651684
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Enhanced descriptions from Syndetics:

Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

Maintaining the standard of excellence set by the previous edition, this lighthearted reference/text surveys the basic geometry of two and three-dimensional spaces stretching student's minds as they learn to visualize new possibilities for the shape of our universe.

Table of contents provided by Syndetics

  • Preface to the Second Edition (p. v)
  • Preface to the First Edition (p. vii)
  • Acknowledgments (p. ix)
  • Part I Surfaces and Three-Manifolds (p. 1)
  • 1. Flatland (p. 3)
  • 2. Gluing (p. 13)
  • 3. Vocabulary (p. 25)
  • 4. Orientability (p. 45)
  • 5. Connected Sums (p. 65)
  • 6. Products (p. 83)
  • 7. Flat Manifolds (p. 99)
  • 8. Orientability vs. Two-Sidedness (p. 125)
  • Part II Geometries on Surfaces (p. 133)
  • 9. The Sphere (p. 135)
  • 10. The Hyperbolic Plane (p. 149)
  • 11. Geometries on Surfaces (p. 157)
  • 12. The Gauss--Bonnet Formula and the Euler Number (p. 165)
  • Part III Geometries on Three-Manifolds (p. 185)
  • 13. Four-Dimensional Space (p. 187)
  • 14. The Hypersphere (p. 199)
  • 15. Hyperbolic Space (p. 213)
  • 16. Geometries on Three-Manifolds I (p. 219)
  • 17. Bundles (p. 229)
  • 18. Geometries on Three-Manifolds II (p. 243)
  • Part IV The Universe (p. 257)
  • 19. The Universe (p. 259)
  • 20. The History of Space (p. 279)
  • 21. Cosmic Crystallography (p. 285)
  • 22. Circles in the Sky (p. 295)
  • Appendix A Answers (p. 309)
  • Appendix B Bibliography (p. 355)
  • Appendix C Conway's ZIP Proof (p. 361)
  • Index (p. 377)

Author notes provided by Syndetics

Jeffrey R. Weeks is a freelance mathematician in Canton, New York. A MacArthur Fellow and the author of numerous scholarly papers on geometry, topology, and cosmology, he splits his time between scientific research with cosmologists hoping to use satellite data to determine the shape of the universe and the development of interactive 3D software and other materials that bring the modern concept of space to middle school, high school, and college students. Dr. Weeks received the A.B. degree (1978) in mathematics from Dartmouth College, Hanover, New Hampshire, and the M.A. (1980) and Ph.D. (1985) degrees in mathematics from Princeton University, Princeton, New Jersey

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