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Experiments in Topology (Dover Books on Mathematics) Paperback – March 1, 1989

by Stephen Barr (Author)

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"A mathematician named Klein
Thought the Moebius band was divine.
Said he: 'If you glue
The edges of two,
You'll get a weird bottle like mine.' " — Stephen Barr

In this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip. Beginning with a definition of topology and a discussion of Euler's theorem, Mr. Barr brings wit and clarity to these topics:
New Surfaces (Orientability, Dimension, The Klein Bottle, etc.)
The Shortest Moebius Strip
The Conical Moebius Strip
The Klein Bottle
The Projective Plane (Symmetry)
Map Coloring
Networks (Koenigsberg Bridges, Betti Numbers, Knots)
The Trial of the Punctured Torus
Continuity and Discreteness ("Next Number," Continuity, Neighborhoods, Limit Points)
Sets (Valid or Merely True? Venn Diagrams, Open and Closed Sets, Transformations, Mapping, Homotopy)

With this book and a square sheet of paper, the reader can make paper Klein bottles, step by step; then, by intersecting or cutting the bottle, make Moebius strips. Conical Moebius strips, projective planes, the principle of map coloring, the classic problem of the Koenigsberg bridges, and many more aspects of topology are carefully and concisely illuminated by the author's informal and entertaining approach.
Now in this inexpensive paperback edition, Experiments in Topology belongs in the library of any math enthusiast with a taste for brainteasing adventures

Experiments in Topology (Dover Books on Mathematics)

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Product Details

Series: Dover Books on Mathematics
Paperback: 238 pages
Publisher: Dover Publications; Reprint edition (March 1, 1989)
Language: English
ISBN-10: 0486259331
ISBN-13: 978-0486259338
Product Dimensions: 7.9 x 5.4 x 0.5 inches
Shipping Weight: 5.6 ounces (View shipping rates and policies)
Average Customer Review: 3.7 out of 5 stars See all reviews (3 customer reviews)
Amazon Best Sellers Rank: #893,979 in Books (See Top 100 in Books)
- #202 in Books > Science & Math > Mathematics > Geometry & Topology > Topology
- #306 in Books > Science & Math > Experiments, Instruments & Measurement > Experiments & Projects
- #3346 in Books > Engineering & Transportation > Engineering > Reference

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Customer Reviews

3.7 out of 5 stars

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22 of 22 people found the following review helpful

Great book for high school teachers and the popular audience

By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on November 16, 2002

Format: Paperback

Written for the beginner in topology but still presupposing a certain amount of mathematical maturity, this book is great fun and should be useful to high school teachers, and those who might be giving public talks on mathematics to audiences who are very interested in mathematics, but who don't have a substantial background in the subject. It is always helpful in those scenarios to have concrete examples that will illustrate some of the more difficult constructions in topology.
In chapter 1, the author attempts to give an intuitive definition of topology. The author uses various pictures and handwaving arguments to explain various notions in topology, such as homeomorphism ("coffee cup = donut"), simply connected (object with no holes), homology (two circles can intersect at one point only), Jordan curves, and Euler's theorem.
In chapter 2, the author uses paper models to illustrate the topology of surfaces, both orientable and nonorientable. The author gives instructions on how to make a paper model of a Klein bottle, but cautions the reader that such a model is not an exact representation of the mathematical object rigorously defined in topology, since the surface passes through itself in the paper construction.
Chapter 3 is a set of instructions on how to make a "shortest" Moebius strip. The procedures for doing this are interesting and fun, for the author constructs a Moebius strip whose length is less than its width, by a factor of 1 over the square root of 3. He devotes an appendix for an improvement due to Martin Gardner of Scientific American fame.
In chapter 4 the author constructs what he calls a "conical Moebius strip".Read more ›

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It has a nice range of expository chapters on a variety of topological ...

By Royal Tenenbaum on October 11, 2015

Format: Paperback

Without wasting too much time with point-set terminology / abstractions, motivates the core subject and explains the "topological way of thinking" from the get go. It has a nice range of expository chapters on a variety of topological subjects, and helps motivate a deeper follow-up study of topology. It seems that modern proofs strive to erase every hint of the the actual insight that allowed the mathematician to arrive at the proof. This book helps remedy that. I took one start off only because the terminology is sometimes vague enough to detract from the readability of the book - it's not clear why cut & paste is allowed in certain situations and not some others, etc.

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16 of 26 people found the following review helpful

useful but not broad enough

By Kevin M. Iga on December 22, 1998

Format: Paperback Verified Purchase

The subject of topology lends itself to many different kinds of experimentation for undergraduate students. But this book spends a disproportionate amount of space on the Mobius strip and related non-orientability issues when it could deal with more knot theory and homotopy theory than it does, and it could introduce finite topologies and Morse theory which abound in self-exploration.

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