Experiments in Topology - Stephen Barr

\nA mathematician named Klein \nThought the Moebius band was divine. \nSaid he: 'If you glue \nThe edges of two, \nYou'll get a weird bottle like mine.' -- Stephen Barr \nIn 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: \nNew Surfaces (Orientability, Dimension, The Klein Bottle, etc.) \nThe Shortest Moebius Strip \nThe Conical Moebius Strip \nThe Klein Bottle \nThe Projective Plane (Symmetry) \nMap Coloring \nNetworks (Koenigsberg Bridges, Betti Numbers, Knots) \nThe Trial of the Punctured Torus \nContinuity and Discreteness (Next Number, Continuity, Neighborhoods, Limit Points) \nSets (Valid or Merely True? Venn Diagrams, Open and Closed Sets, Transformations, Mapping, Homotopy) \n \nWith 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. \nNow 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.\n