Talk:Möbius strip

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Talk:Möbius_strip/Archive 1

Contents 1 Mobius strip with circular boundary 2 Objection presented by Dr. Mugrabi, psychoanalyst: Relying us on the surface's definition, to speak of “two faces” of one surface, shows simply something that we must understand like stupidity. According with Descartes, nor God could give to return 180° a surface to arrive at Another Side of one surface. 3 3D versus 2D 4 Cutting Concerns

[edit] Mobius strip with circular boundary

I found the following reference online. "D. Lerner and D. Asimov. The sudanese mobius band. (video). In SIGGRAPH Video Review, 1984." Does anybody have access to this video? I'd love to see some stills! Sam nead 00:30, 6 September 2006 (UTC)

[edit] Objection presented by Dr. Mugrabi, psychoanalyst: Relying us on the surface's definition, to speak of “two faces” of one surface, shows simply something that we must understand like stupidity. According with Descartes, nor God could give to return 180° a surface to arrive at Another Side of one surface.

[edit] 3D versus 2D

Could someone please answer me this:

If you put a hole in the m�bius strip, where does it go to? It goes through the strip and to the same side it started. How does that work?

"Where does it go to?" To "go" somewhere, you have to go "through" something. That is, you are assuming that the Mobius strip has some thickness. It doesn't.

If you do insist that the strip has some thickness (atoms, etc) then you are treating it like a solid, three-dimensional object, and not like a surface. Again there is no mystery: lots of three-dimensional things have only one side, like an orange or a bagel. Sam nead 16:58, 15 April 2006 (UTC)

The m�bius strip is a surface in three dimentions, and each point on the strip is part of two areas on the strip. Thus, removing the points on an area of the strip would create two breaks in a line drawn around the strip. --Roger Chrisman 22:40, 4 September 2006 (UTC)

Imagine a piece of thick paper, 10 mm wide, 0.5 mm thick, and however long you want. I give the end a half-twist and join the ends together in whatever normal or magical way you like. This is unquestionably a 3D object, being that it has a 0.5 mm thickness. But as far as I can tell, this does not prevent it from having any of the amazing properties of a legitimate mobius strip. If one makes a hole in it, that hole starts on one side, goes through the thickness of the paper, and ends up on the SAME side!!! And you can prove it is the same side, by crawing the line as described in the article! Anyone have a problem with that? That's why I say that a mobius strip is (or can be) a 3D object. --Keeves 00:43, 5 September 2006 (UTC)

Keeves: What you are describing is three-dimensional, but it is not a Mobius strip. Mobius strips are surfaces, and so are two dimensional. Said another way -- a Mobius strip is a mathematical abstraction and not a real object. It is a special kind of surface. Sam nead 03:22, 5 September 2006 (UTC)

Roger: The Mobius strip need not be embedded in three-space. It is a "space" all on its own. Sam nead 03:22, 5 September 2006 (UTC)

I stand corrected. Thanks! --Keeves 16:14, 5 September 2006 (UTC)

I view the mobius is more like 3cm wide, 10cm long and 0cm high.

[edit] Cutting Concerns

Alternatively, if you cut along a Möbius strip about a third of the way in from the edge, you will get two strips: One is a thinner Möbius strip - it is the center third of the original strip. The other is a long strip with two half-twists in it (not a Möbius strip) - this is a neighborhood of the edge of the original strip.

This contridicts what is said above:

If the strip is cut along the above line, instead of getting two separate strips, it becomes one long strip with two half-twists in it (not a Möbius strip). This happens because the original strip only has one edge which is twice as long as the original strip of paper. By cutting you have created a second independent edge, half of which was on each side of the knife or scissors. If you cut this new, longer strip down the middle, you get two strips wound around each other.

Right? There the same steps. Joerite 04:23, 1 October 2006 (UTC)

You lost some context for the second quote: "the above line" was drawn in the middle (half-way from the edge), not ⅓ from the edge. Try it for yourself and see what happens:) It sounds weird, and perhaps counterintuitive to people not familiar with the Möbius strip, which is why it's mentioned. DMacks 16:09, 1 October 2006 (UTC)

So cut halfway across the width and you get one strip, but cut one third of the way and you get two strips? What happens at 2/5 of the way across? 3/7 of the way? 4/9? Seems fishy to me - how close do you have to get to "halfway" before you end up with one strip? Where did I put those scissors....?143.252.80.100 21:15, 21 November 2006 (UTC)

Interesting thought experiment. I think what actually happens if you cut 1/3 of the way across, is, when you get all the way around once your scissors WON'T intersect your starting point. Instead you'll be at the 2/3 point, and can continue cutting all the way around again, until you do get back to the 1/3 point. But wouldn't that give you THREE strips when you do get back to the start? That doesn't make any sense either, though...when you finally finish the cut you're clearly only separating two strips. Help, my head is going to explode! Middlenamefrank 21:26, 21 November 2006 (UTC)

You're right in that the "first" time around, you wind up 2/3 across. As I visualize it more generally, the issue is that there is only one edge (in the sense of a normal sheet of paper) on the strip. So if you start "some distance x from the edge", when you have traveled once around the loop, you are now that same distance from the edge, but now "the edge" is now across the loop from where it was when you started. You haven't really crossed' the middle so much as wrapped around it. So you peel the edges off the strip as one loop and leave the middle section as the other loop. DMacks 22:08, 21 November 2006 (UTC)

There's nothing particularly special about 1/3. The point is whether you cut along the center circle or not. If you cut along the center circle, you will get an orientable band. If you basically trim off the edge (cutting along some distance less than half the width of the band) when you come once around, you find you need to make another trip around to finish off the cutting. Of course, if you decide not to go around again, but just join the ends of the cut together, that's fine and gives you the same result as cutting along the center circle. In real life, where you can't really cut along the exact center (everything is approximate), that's what you're really doing. That should answer your question about how close you can get. If you get close enough, when cutting you will probably decide to join up the cut after only one trip around the band because the ends of the cut are close enough. --Chan-Ho (Talk) 08:29, 22 November 2006 (UTC)