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# Paper Trick: Newsletter Challenge (04/26/05)

Posted April 26, 2005 7:00 AM

The question as it appears in the 04/26 edition of Specs & Techs from GlobalSpec:

Using a piece of paper, what structure can you make that has only one side? If you cut it down the middle, what happens? And what if you then cut it down the middle again?

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The Engineer

Join Date: Feb 2005
Location: Albany, New York
Posts: 5170
#1

### My Guess

04/26/2005 4:58 PM

If you twist the paper and tape the ends together, you create a Mobius Strip which has one side. Cut it and you have two sides. Cut it again, you've got two objects with two sides.

Participant

Join Date: Apr 2005
Posts: 1
#2

### Re:My Guess

04/27/2005 8:40 PM

He's Right:

Commentator

Join Date: Apr 2005
Posts: 71
#3

### Re:My Guess - working backwards

05/04/2005 7:58 AM

Maybe there's a bored topologist out there who can answer this for me: Starting backwards, if you start with the two strips that are looped and weld their edges together, you get a single strip with a full twist. Weld the edges of this strip together and you get a Moebius strip. So if you then weld the edge of the Moebius strip to itself, do you get a Klein bottle -- an object with one surface but no edges? Seems to me you'd be going from 4 surfaces and 4 edges, to 2 surfaces and 2 edges, to 1 surface and 1 edge, to 1 surface and no edge. Or maybe the object mathematically has no surface (?) and no edge?

Guru

Join Date: Mar 2007
Location: Etherville
Posts: 12334
#5

### Re:My Guess - working backwards

07/21/2009 2:38 PM

I'm having a hard time visualizing it, but a Moebius strip can be welded into a Klein bottle. Ref.

The Science Museum in London has an excellent section on topology. I'll possibly be there within the next few weeks, so I'll see if any of their models illustrate this.

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Friend of CR4

Join Date: Dec 2004
Posts: 1995
#4

05/12/2005 2:51 PM

As written in the 5/03 issue of Specs & Techs from GlobalSpec:

The structure is referred to as a "Möebius strip" (or Möebius band), named for A. F. Möebius (1790-1868), a mathematician and astronomer. To construct a Möebius strip, take a strip of paper, twist it 180° and fasten the two ends together. There is only one side to this structure. If you then cut it down the middle, it changes from single-sided to double-sided. And cutting this double-sided structure down the middle results in two double-sided loops. Try it! (Or have your kids try it...)

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