The Shape of Space (Chapman & Hall/CRC Pure and Applied Mathematics) [Hardcover]

Jeffrey R. Weeks (Author)

Book Description

ISBN-10: 0824707095 | ISBN-13: 978-0824707095 | Publication Date: December 15, 2001 | Edition: 2nd

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.

Product Details

• Hardcover: 328 pages
• Publisher: CRC Press; 2nd edition (December 15, 2001)
• Language: English
• ISBN-10: 0824707095
• ISBN-13: 978-0824707095
• Product Dimensions: 9.5 x 6.6 x 1.2 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.9 out of 5 stars  See all reviews (11 customer reviews)
• Amazon Best Sellers Rank: #193,988 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

54 of 54 people found the following review helpful:

5.0 out of 5 stars Straight talk about curved space, February 9, 2002

By 

Royce E. Buehler "figvine" (Cambridge, MA USA) - See all my reviews
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This review is from: The Shape of Space (Chapman & Hall/CRC Pure and Applied Mathematics) (Hardcover)

What is the universe as a whole shaped like? Does it curve back on itself? Does it meet itself at the other side without curving? Is its Flatland analogy a plane, or a sphere, or a doughnut, or a Klein bottle? What other, stranger geometries become possible with the added dimension? And if the universe has one of these exotic shapes, how could astronomers ever know for sure?

Jeffrey Weeks, a MacArthur ("genius grant") fellow and a consultant to NASA on cosmological observations, believes that there's no reason why a liberal arts student or a high schooler shouldn't be able to have a solid understanding of the answers to these questions, even though some of them are at the edge of research in cosmology and three-manifolds, and others have traditionally not been part of the math curriculum before graduate school.

The math is presented at an elementary level, but it is genuine mathematics. Readers in the intended audience must be prepared to roll up their sleeves; there are exercises, and there are formulas, and their minds will be stretched. But there are no prerequisites other than a little first-year algebra, and the discussion stays at a vividly concrete level, with a plethora of diagrams to aid the swelling imagination. High schoolers will benefit from some guidance getting through it; it's appropriate for undergraduate self-study.

More mathematically sophisticated readers, even those who've taken a course in algebraic topology or differentiable manifolds, will find the book a lively read, but will still probably learn a thing or two. I, for one, was startled to be shown a Moebius strip that was two-sided! (The trick is to embed it in a non-orientable three-space.)

The payoff is in the final two chapters, which detail programs of astronomical observation that could well tell us the precise topology and geometry of the universe, and explain just how they would do it. One chapter is devoted to a technique based on correlating distances between galactic clusters, and the other to a statistical search for correlated arcs of great circles in the cosmic microwave background. Both observations will probably be completed within the next decade. It's an exciting prospect.

Buyers note: I believe the Amazon characterization of this as a paperback is in error. I bought the second edition in hardcover at the same list price. In its (successful) attempt to avoid intimidation, it uses a large typeface, so it would fill out some 200 pages in a more typical math format.

40 of 40 people found the following review helpful:

5.0 out of 5 stars Loads of fun, April 19, 2002

By 

Chan-Ho Suh (California) - See all my reviews
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This review is from: The Shape of Space (Chapman & Hall/CRC Pure and Applied Mathematics) (Hardcover)

But this book can also be quite serious, although it may take someone with an extensive math background to see this. The book seems aimed primarily at high-schoolers, but graduate students in topology can definitely benefit from reading it.

Weeks starts out by explaining surfaces and the quotient space descriptions of the torus and klein bottle. Later chapters describe 3-manifolds, fibre bundles(!), and the 8 geometries relevant to Thurston's geometrization conjecture. The focus of the book is on applying these concepts to investigating the shape of our spatial universe. This is a particularly apt goal, given that many times in the book the reader is asked to imagine living in various kinds of spaces.

He has a very good set of exercises designed to increase one's visualization powers. For example, in the chapter on 3-manifolds, he has the reader color various covering space pictures of 3-manifolds like the 3-torus, according to some specifications; this really helps one understand how covering maps work.

As someone who was familiar with topology before reading the book, I can say that the book has definitely increased my understand of 3-manifolds, which is more than I can say for most topology books. In particular, I found the material on fibre bundles very enlightening.

15 of 15 people found the following review helpful:

5.0 out of 5 stars Topology for everyone, July 25, 2003

By 

Debajyoti Ray (Toronto, ON Canada) - See all my reviews

This review is from: The Shape of Space (Chapman & Hall/CRC Pure and Applied Mathematics) (Hardcover)

Jeffrey wrote this book with the high school student in mind, but even as a second year student in Mathematics I found this book quite informative. Most textbooks in Analysis or Topology do not give you an intuitive feel for the subject. I recommend this book for anyone taking a course in Topology, even Graduate students.
This book is well written with many illustrations and exercises to help you get an intuitive understanding of 3 Dimensional manifolds. This helped me a lot in my second year Analysis class as I had an intuitive notion of manifolds taught in class.
At the same time the book is easy enough for high school students who always wondered what a Mobius strip or a Klein bottle was but did not find any books on it. This book would make Topology interesting for everyone. I give it a five star rating.