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25 Remote Warehouse Mathematics- Geometry and Trigonometry

Experiments in Topology

by

Experiments in Topology Cover

 

Synopses & Reviews

Publisher Comments:

"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

Synopsis:

Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.

Synopsis:

With this book and a square sheet of paper, the reader can make paper Klein bottles; 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 other aspects of topology are clearly explained.

Table of Contents

1 What is Topology?

    Euler's Theorem

2 New Surfaces

    Orientability

    Dimension

    Two More Surfaces

    The Klein Bottle

3 The Shortest Moebius Strip

4 The Conical Moebius Strip

5 The Klein Bottle

6 The Projective Plane

    Symmetry

7 Map Coloring

8 Networks

    The Koenigsberg Bridges

    Betti Numbers

    Knots

9 The Trial of the Punctured Torus

10 Continuity and Discreteness

    "The "Next Number"

    Continuity

    Neighborhoods

    Limit Points

11 Sets

    Valid or Merely True?

    Venn Diagrams

    Open and Closed Sets

    Transformations

    Mapping

    Homotopy

  In Conclusion

  Appendix

  Index

Product Details

ISBN:
9780486259338
Author:
Barr, Stephen
Publisher:
Dover Publications
Location:
New York :
Subject:
General
Subject:
General science
Subject:
Science
Subject:
Geology
Subject:
Geometry - General
Subject:
Topology
Subject:
General Science
Subject:
Mathematics-Geometry and Trigonometry
Subject:
Applied
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
v. 136, art. 15
Publication Date:
19890331
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
238
Dimensions:
8.5 x 5.38 in 0.65 pd

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Science and Mathematics » Mathematics » Topology

Experiments in Topology New Trade Paper
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Product details 238 pages Dover Publications - English 9780486259338 Reviews:
"Synopsis" by ,
Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.
"Synopsis" by ,
With this book and a square sheet of paper, the reader can make paper Klein bottles; 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 other aspects of topology are clearly explained.

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