THE MOEBIUS AND THE KLEIN

The Möbius Strip is a good introduction to how strange and odd topology is. You can make a Möbius strip by taking a simple length of paper, let’s say 2 cm wide by 20 cm long, and twisting one end one half turn then joining the two ends together. The intriguing result is that the strip has lost one of its two edges and one of its two surfaces. Trace your finger around the surface and you will see that it is now a 2-dimensional creature with one side and one edge sitting very comfortably in our 3-dimensional world. Very cool. Now make another with the opposite twist and join them together along their edges to make a Klein bottle.  Oops ….impossible in our world, you need to go to 4-space, the curious and enticing hinterland of topology.

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