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Questions tagged [mobius-band]

The Möbius band or Möbius strip is a surface with only one side and only one boundary. The Möbius strip has the mathematical property of being non-orientable. It is named after the German mathematician August Ferdinand Möbius.

The Möbius band or Möbius strip is a surface with only one side and only one boundary (a simple closed curve which means it is homeomorphic to a circle). The Möbius strip has the mathematical property of being non-orientable. It is named after the German mathematician August Ferdinand Möbius. The Euler characteristic of the Möbias strip is zero.

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Is there a maximum width for a Möbius strip?

The Möbius strip is made by rotating one of the ends of a 2D strip 180° and then glueing these together. I was wondering, how wide can the strip be? For example, can we still make a Möbius strip from a square? Making a Möbius strip by rotating the…
Deschele Schilder
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Derive Cartesian cubic Möbius strip from parametric

The following link: http://mathworld.wolfram.com/MoebiusStrip.html shows the Möbius strip parametrized as \begin{eqnarray} x = [ R + s \cos \left ( \frac{1}{2} t \right ) ] \cos t \\ y = [ R + s \cos \left ( \frac{1}{2} t \right ) ] \sin t \\ z = s…
Herman Jaramillo
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Why It's said to be that when a Flatlander makes a turn around a Möbius Strip, their internal organs are reversed, while they turn upside down?

I mostly hear that a flatlander becomes their mirror counterpart when they make a turn inside it. Though for that to happen, they need to be turned upside down. Does it not make a difference when they are turned upside down inside 2D world? If so,…
Deha Ortasarı
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Möbius bundle no global trivialization

I there! I am trying to write down why the Möbius bundle has no global trivialization. I just read that there is none but I want to see a written prove for this. I am not even sure which definition of the Möbius strip would be the best. First let…
JDoe
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Which is the actual surface of a Möbius strip?

Usually, the pop explanations of the properties of the Möbius strip say that if you take a pencil and start drawing a line in the middle of the strip, you'll have to make two complete loops to return to the original position. But if you look at the…
mau
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Is this image a direct sum of two Moebius bands?

If we just look at the exterior surface of this, and view it as a 2-manifold, is this the direct sum of two Mobius bands? I see that this object has 2 sides and is orientable. If we view it as a 3-manifold, is that what makes it a direct sum of two…
locally trivial
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