These correspond to stitching 0, 1, 1 and 2 opposite edges of a square, giving a Klein bottle in two cases.
32.
The underlying compact manifold has boundary a Klein bottle, and the first homology group of the Gieseking manifold is the integers.
33.
A similar nontrivial bundle is the Klein bottle which can be viewed as a " twisted " circle bundle over another circle.
34.
The hypothetical object known as a Klein bottle plays an important role in the book after Peter visits the London Science Museum.
35.
At Number Heaven, Robert learns of imaginary numbers, which Teplotaxl describes as " imaginative numbers ", as well as the Klein bottle.
36.
For instance, the Lens space L ( 4, 1 ) contains an incompressible Klein bottle that is not \ pi _ 1-injective.
37.
Philip Franklin ( 1930 ) proved that the Klein bottle requires at most 6 colors, rather than 7 as predicted by the formula.
38.
To construct the Klein Bottle, glue the red arrows of the square together ( left and right sides ), resulting in a cylinder.
39.
For example, the one-holed toroid and the Klein bottle both have ? = 0, with the first being orientable and the other not.
40.
He also hand-blows Klein bottles, oddly shaped flasks that theoretically exist only in the fourth dimension because their inside is also their outside.
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