Started on 18:14 on this video(problem 1), A professor mentioned he could make a topological object with a single piece of paper and without glue, how are you able to make it? By the way, how does that have to do with the theory of topology. link: http://www.youtube.com/watch?v=Ap2c1dPyIVo&feature=related
How to make this topological object with a single piece of paper and without glue?
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general-topology
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0Oh - you're right. Well seen. – 2012-04-07
1 Answers
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This is an oldie but goodie. Cut along the indicated three lines. Fold one of the dotted lines one way, and the second one in the reverse direction.
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0@Danica: you are correct, and that is an astute observation. The point here is that the obvious map from a paper to a paper with a partial cut in it is not a homeomorphism. There is a more subtle map that takes the original paper to the partially cut paper. The boundary of the original paper would now travel up one side of the cut and down the other side. I hope that helps! – 2012-10-25