Experiments in Topology

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.

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