

8


][

infinity in a single character.

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Mandy

heh, true that.

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User24

like a mobius strip (you can make those out of paper, by the way)

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spoons

is my favorite number

030522


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( ... )

so can anyone tell me what happens when you cut a mobius strip all the way around, the long way? why? what if you keep your cut 1/3 of the way from the edge the whole time?

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spoons

If you cut it in the middle you end with a mobius strip twice as large as the you began with. Why? Simply becuase when you cut it down the center you end where you started and because of the twist you never cut completely across the paper....and when you cut it by a third you just keep cutting until you cant cut anymore because you never end where you start...I dunno they arent to difficult to make... knock your socks off

030523


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more: what happens when you sew the edge of a mobius strip to the edge of a disc (of paper or what have you)? what happens when you sew the edges of two mobius strips together?

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spoons

eek! For both of these I got three very angry mobius strips! The two obviously couldnt be completely overlapped because of the way the twisty worked and the one on the disk could be "sewn" on but it would have a twist in it and never lay flat. eek I guess im not too sure the point of that one but youre very clever.

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the first one's called a "boy surface"... http://mathworld.wolfram.com/BoySurface.html it's a form of the real projective plane. the second makes a klein bottle. http://mathworld.wolfram.com/KleinBottle.html i'm not particularly clever, i just took a course in topology.

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and in the wee hours of the prague morning a foreign math postdoc was making joke about a waitress bringing klein bottle full of wine and coming back with just her two cross caps..

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user24

"A surface such as the Möbius strip or Klein bottle (Gray 1997, pp. 322323) on which there exists a closed path such that the directrix is reversed when moved around this path. The real projective plane is also a nonorientable surface, as are the Boy surface, crosscap, and Roman surface, all of which are homeomorphic to the real projective plane (Pinkall 1986)." wow. numbers are cool.

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crOwl

one more than 7 as if you think the perfect number is faerie tale.

040727



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