Overview

"""""A mathematician named KleinThought the Moebius band was divine.Said he: 'If you glueThe edges of two,You'll get a weird bottle like mine.' """" - Stephen BarrIn 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 StripThe Conical Moebius StripThe Klein BottleThe Projective Plane (Symmetry)Map colouringNetworks (Koenigsberg Bridges, Betti Numbers, Knots)The Trial of the Punctured TorusContinuity 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 colouring, 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 in the byways of mathematics."

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9780486259338

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Reviews

Topology is a difficult to define branch of advanced mathematics that has more bearing on math courses today than it did when outer space was out-of-bound??. In one sense it is the study of continuity: beginning with space, or shapes, it generalizes, and then by analogy leads into other kinds of continuity - and space as we generally understand it - is left far behind. Although really high-bouncing topologists not only avoid anything like pictures of these things... the book is generously illustrated with explanatory figures to support the introductory text. The author, who must take the student from the realm of the tangible and measurable to that of the abstract, keeps a light heart and his tongue in his cheek throughout the book. He keeps his explanations and examples as clearly worded as possible. While the book is not difficult to read, the subject is not an easy one to follow. The audience will be limited, but for the elite of the math class, this book is the one of its kind. (Kirkus Reviews)

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