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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

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  • $\begingroup$ @mixedmath - i have no idea how to do it. $\endgroup$
    – Victor
    Apr 7, 2012 at 1:31
  • $\begingroup$ but have you tried? He tells you that you make exactly 2 cuts, and you fold the paper, and that's all. $\endgroup$
    – davidlowryduda
    Apr 7, 2012 at 1:34
  • $\begingroup$ @mixedmath - i missed the part you mention me in the video, but after i tried i still not getting it. $\endgroup$
    – Victor
    Apr 7, 2012 at 1:41
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    $\begingroup$ Actually, I think you need 3 cuts. $\endgroup$
    – Dejan Govc
    Apr 7, 2012 at 2:19
  • $\begingroup$ @DejanGovc - How? $\endgroup$
    – Victor
    Apr 7, 2012 at 2:26

1 Answer 1

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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.

enter image description here

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  • $\begingroup$ beat me to it :) $\endgroup$
    – t.b.
    Apr 7, 2012 at 2:34
  • $\begingroup$ +1 for excellent answer, but how does that relate to the course of topology? $\endgroup$
    – Victor
    Apr 7, 2012 at 2:46
  • $\begingroup$ @Victor: Well, once you make the three cuts you get a topological space homeomorphic to a disk. The folds don't matter from the topological perspective. Not sure what point Wildberger was trying to make with this. $\endgroup$ Apr 7, 2012 at 2:48
  • $\begingroup$ @t.b. yours is a mirror image of mine. Perhaps that counts as a different answer. :) $\endgroup$ Apr 7, 2012 at 2:49
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    $\begingroup$ maybe :) @Victor: I see the point of the exercise on a much more basic level than Jim: in my opinion spatial imagination and intuition is one of the very crucial prerequisites for doing (algebraic) topology and all sorts of other math. Train it, look at knots, for example. $\endgroup$
    – t.b.
    Apr 7, 2012 at 2:56

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