Talk:Möbius strip: Difference between revisions
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:I apologise, I think I was wrong. I was regarding a mobius band as not just a 2D rectangle cuved round into a circle and twisted, but also as 3D prisms curved round and twisted. These result in shapes with one side and one edge just as a mobius band does, and I believed they all fell under the same name. At simplest you can have a triangular prism, but a prism with many sides approaches a torus. Similarily, the simplest [[sphericon]] is based on a sixty degree apexed cone split and twisted, and a more complex sphericon approaches a sphere. What page would you reference it to? |
:I apologise, I think I was wrong. I was regarding a mobius band as not just a 2D rectangle cuved round into a circle and twisted, but also as 3D prisms curved round and twisted. These result in shapes with one side and one edge just as a mobius band does, and I believed they all fell under the same name. At simplest you can have a triangular prism, but a prism with many sides approaches a torus. Similarily, the simplest [[sphericon]] is based on a sixty degree apexed cone split and twisted, and a more complex sphericon approaches a sphere. What page would you reference it to? |
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:You could add it to [[List of polygons, polyhedra and polytopes]], perhaps as a 'see also'; also to the [[list of geometry topics]] under the 3D shapes. |
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[[User:Charles Matthews|Charles Matthews]] 20:01, 9 Apr 2004 (UTC) |
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Revision as of 20:01, 9 April 2004
Axeeeeeel. Nice work. One day I'll put some pictures with strip and some outstanding Maple code or something like that.FireJamXRasta 3 Wednesday [2002.02.27]
Wouldn't it be cool to have a small java applet of the moebius strip in 3D?
- Yes, (and Maple or Mathematica code too)
I took out the R from the parametrization for three reasons:
- It was not explained.
- It looked as if it was a parameter, but it was in fact a fixed number representing the radius of the Möbius band.
- Not all values of R work (you can get self intersections if R is too small.
I explained the parametrization a bit better. AxelBoldt
- Nice Axel. Yes R seems to be a constant and not a parameter. We should investigate for which R Moebius strip is really defined. I would like to say something more: I didn't mean that those presumptions about connection Universe<->Moebius strip come from SF - they come from science world (physics, cosmology) I guess. We should correct that fact somehow. Uh, Axel I don't want to be your student, ha, ha. I still owe to this page another picture of a strip... XJam [2002.03.25]] 1 Monday (0)
- I haven't seen any serious cosmology suggesting a Moebius strip universe, but if you find anything, make sure to put it in the article. AxelBoldt
I have checked 'very briefly' for R. As it seems strip degenerate near 0 and probably R must be positive or non-positive real number. Very intersting - how small should R be to get self intersections. We can also split R to R1 and R2. Does any self intersection appear if R1 = - R2. (I guess not - but how can you be shure?) Another output picture is coming...
XJam [2002.03.26]] 2 Tuesday (0)
The Klein bottle isn't a 3D analogue, since it's also a surface -- it's more an extension. -- Tarquin
I have a question regarding
- Another equation for a Möbius strip is log(r)*sin(θ/2)=z*cos(θ/2).
I assume this is in cylindrical coordinates (r,θz)? This equation describes an unbounded figure though (you can enlarge r and z beyond all bounds), so I don't see how it can describe a Moebius strip. AxelBoldt, Sunday, June 2, 2002
It is in cylindrical coordinates. It describes an unbounded Moebius strip. If you want a bounded strip, you can take the part inside a torus, or restrict r and z. --phma
moebius in fiction: there's also A Subway Named Moebius, AJ Deutsch.
Am I the only person bothered by the phrase "Mobius strip is a topological object with only one surface"??? What does this mean??? I know what it is meant to mean, (i.e. that it's not orientable), and that this is the way to put it in as comfortable a language as possible, but the way it's phrased this way it seems too inaccurate (or meaningless) to be worth the benefit. Revolver 10 Nov 2003
Harmless in the intro, I'd say. Anyone reading on is given a clearer idea. Generally speaking the first para of an article has some license to use looser language, and not to define everything with exactitude. There again, the surface link is probably unhelpful there.
Charles Matthews 18:00, 10 Nov 2003 (UTC)
I removed this:
A family of 3D solids that closely relate to Möbius strips are the Sphericons. They are like a Möbius band, but without the hole in the middle. If you make a Möbius band out of a n-sided polygon sectioned strip, rotate it k amount and count the number of sides and edges created, more parallels can be found with the Sphericon.
I'm convinced at this point that the sphericon is that closely related; certainly not topologically.
Charles Matthews 13:48, 7 Apr 2004 (UTC)
- I apologise, I think I was wrong. I was regarding a mobius band as not just a 2D rectangle cuved round into a circle and twisted, but also as 3D prisms curved round and twisted. These result in shapes with one side and one edge just as a mobius band does, and I believed they all fell under the same name. At simplest you can have a triangular prism, but a prism with many sides approaches a torus. Similarily, the simplest sphericon is based on a sixty degree apexed cone split and twisted, and a more complex sphericon approaches a sphere. What page would you reference it to?
- You could add it to List of polygons, polyhedra and polytopes, perhaps as a 'see also'; also to the list of geometry topics under the 3D shapes.
Charles Matthews 20:01, 9 Apr 2004 (UTC)