Experiments in Topology - Brossura

Barr, Stephen

Brossura

ISBN 10: 0486259331 ISBN 13: 9780486259338

Casa editrice: Dover Pubns, 1989

Riassunto

"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 in the byways of mathematics.

Su questo libro

Contenuti:

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 Description:

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.

Su questa edizione

• Editore: Dover Pubns
• Data di pubblicazione: 1989
• ISBN 10: 0486259331
• ISBN 13: 9780486259338
• Rilegatura: Copertina flessibile
• Numero di pagine: 210