ABSTRACT

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.

chapter |2 pages

PART I Surfaces and Three-Manifolds

chapter 1|10 pages

Flatland

chapter 2|12 pages

Gluing

chapter 3|20 pages

Vocabulary

chapter 4|8 pages

Orientability

chapter XXX|12 pages

X X X

chapter 5|18 pages

Connected Sums

chapter 6|16 pages

Products

chapter 7|34 pages

Flat Manifolds

part |2 pages

Part II Geometries on Surfaces

chapter 9|3 pages

The Sphere

chapter |11 pages

__±X

chapter 10|16 pages

The Hyperbolic Plane

chapter 14|14 pages

The Hypersphere

chapter 15|16 pages

Hyperbolic Space

chapter 17|28 pages

Bundles

part |2 pages

Part IV The Universe

chapter 19|20 pages

The Universe

chapter 20|16 pages

The History of Space

chapter 22|10 pages

Circles in the Sky

chapter |4 pages

rB c

chapter |4 pages

Appendix A

Answers

chapter |40 pages

> A >

chapter |2 pages

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