"A mathematician named Klein
Thought the Moebius band was once divine.
Said he: 'If you glue
The edges of two,
You'll get a unusual bottle like mine.' " — Stephen Barr
In this energetic booklet, the vintage in its box, a grasp of leisure topology invitations readers to enterprise into such tantalizing topological geographical regions as continuity and connectedness through the Klein bottle and the Moebius strip. starting with a definition of topology and a dialogue of Euler's theorem, Mr. Barr brings wit and readability to those topics:
New Surfaces (Orientability, measurement, The Klein Bottle, etc.)
The Shortest Moebius Strip
The Conical Moebius Strip
The Klein Bottle
The Projective aircraft (Symmetry)
Networks (Koenigsberg Bridges, Betti Numbers, Knots)
The Trial of the Punctured Torus
Continuity and Discreteness ("Next Number," Continuity, Neighborhoods, restrict Points)
Sets (Valid or in simple terms precise? Venn Diagrams, Open and Closed units, changes, Mapping, Homotopy)
With this e-book and a sq. sheet of paper, the reader could make paper Klein bottles, step-by-step; then, through intersecting or slicing the bottle, make Moebius strips. Conical Moebius strips, projective planes, the main of map coloring, the vintage challenge of the Koenigsberg bridges, and plenty of extra points of topology are rigorously and concisely illuminated by way of the author's casual and enjoyable approach.
Now during this low-cost paperback version, Experiments in Topology belongs within the library of any math fanatic with a style for brainteasing adventures within the byways of mathematics.