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 '12 at 1:31
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$\begingroup$ 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 '12 at 1:34
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$\begingroup$ @mixedmath - i missed the part you mention me in the video, but after i tried i still not getting it. $\endgroup$ – Victor Apr 7 '12 at 1:41
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2$\begingroup$ Actually, I think you need 3 cuts. $\endgroup$ – Dejan Govc Apr 7 '12 at 2:19
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$\begingroup$ @DejanGovc - How? $\endgroup$ – Victor Apr 7 '12 at 2:26
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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.
answered Apr 7 '12 at 2:32
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$\begingroup$ +1 for excellent answer, but how does that relate to the course of topology? $\endgroup$ – Victor Apr 7 '12 at 2:46
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$\begingroup$ @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. $\endgroup$ – Cheerful Parsnip Apr 7 '12 at 2:48
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$\begingroup$ @t.b. yours is a mirror image of mine. Perhaps that counts as a different answer. :) $\endgroup$ – Cheerful Parsnip Apr 7 '12 at 2:49
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2$\begingroup$ 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 '12 at 2:56
