Synopses & Reviews
"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)
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
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.
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.
Table of Contents
1 What is Topology?
2 New Surfaces
Two More Surfaces
The Klein Bottle
3 The Shortest Moebius Strip
4 The Conical Moebius Strip
5 The Klein Bottle
6 The Projective Plane
7 Map Coloring
The Koenigsberg Bridges
9 The Trial of the Punctured Torus
10 Continuity and Discreteness
"The "Next Number"
Valid or Merely True?
Open and Closed Sets