# 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.

112 questions
Filter by
Sorted by
Tagged with
57 views

### Möbius Strip + Möbius Strip = Klein Bottle, What about Klein Bottle + Klein Bottle =?

We know that 2 Möbius-Strips can be joined edge-wise to eliminate that edge producing 0 Edge topological structure. ML (Möbius Left) + MR (Möbius Right) = KOJ (Simple "inverted sock" Klein ...
35 views

### Does this count as a loop on Möbius strip

Suppose we take the Möbius strip as $X = \frac{[0, 1]\times[0, 1]}{\sim}$ with usual equivalence relation. If I define $\alpha: [0, 1] \rightarrow X$ by $x \rightarrow [(x, 1/2)]$, is this a loop? ...
23 views

### 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-...
53 views

### Möbius strips with 3 twists to make a Klein bottle

I've been looking into Klein bottles and Möbius strips. What would happen if you took two "Möbius" strips with three twists in them, each oriented opposite eachother, and then connected the edges. ...
47 views

### Sphere with 1 disk removed and replaced with a Möbius strip

1) I read that a Klein bottle is in fact a sphere with 2 disks removed and replaced by Möbius strips. I find it hard to imagine how this constructs a Klein bottle. Any ideas how I can convince myself ...
65 views

### Proving homeomorphism in Möbius strip

Consider the Möbius strip defined by the following equivalence relation on the subspace $[0,1]\times]-a,a[$ of $\mathbb{R}^2$: $$(x,y)\sim (x',y')\implies (x,y)=(x',y')\vee|x'-x|=1\:\text{and}\:y'=-y$$...
24 views

### Orientation of a vector space

I want to open this question with a disclaimer, that I am not a native english speaker and I did not study linear algebra in english, and am simply trying to use words that I believe best translate ...
28 views

### Viewing Manifolds as Embedded in Euclidean Space

In learning differential topology I've been exposed with two methods of defining and working with manifolds: The more concrete but initially less general approach of Guillemin and Pollack, where all ...
102 views

34 views

### normal vector can not constructed at a point of a surface?

In page 66, chap 9 of the book "classical mechanics point particles and relativity" of Walter Greiner, say: "A surface for which a normal vector may be constructed at any point is called orientable." ...
44 views

### 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 ...
76 views

61 views

### Do parallel, angle, triangle, area etc still apply in Mobius band?

Normal geometry concepts, such as parallel, angle, area, triangle, do they still apply in Mobius band? If not, in which case will they fail to do so? For example, what would three lines on a Mobius ...
148 views

### possible number of sheets for a Moebius band covering

Let M be the Moebius band, identified by the quotient of $[0,1]\times [0,1]$ by the equivalence $(x,0) \sim (1-x,1)$. Let $p: M\to M$ be a covering and $n$ its number of sheets. Find the possible ...
135 views

### is every path-connected covering of the Moebius strip a Galois cover?

Let $p : E → M$ be a covering of $M$ the Moebius Sttrip such that $E$ is path connected. Is this a Galois covering? My intuition is there must be some non locally path connected coverings that are ...
142 views

### Mobius strip with constant negative curvature

Is there any simple model of the Mobius strip with a constant negative Gaussian curvature? There is an example on Wikipedia (https://en.wikipedia.org/wiki/M%C3%B6bius_strip#Open_M%C3%B6bius_band), but ...
66 views

### Twisted Ring homeomorphic to Möbius Band?

Is the following parameterized surface homeomorphic to a Möbius Band? ...
96 views

### Twisting the unit square n times before gluing( 2.1.6 in G&P).

The question is given below: I have made a Mobius band with a paper and twisted it 3-times but I could not describe what I see it may be a 3 knot shape, could anyone give me a hint for solving that ...
177 views

### Group action of $\mathbb Z$ on infinite strip is homeomorphic to the Mobius Band

I am trying to prove that: Given $X=R×[-1, 1]$ and the action of $\mathbb Z$ as $m(x,y)=(x+m, (-1)^m y)$, prove that the space $X/Z$ is homeomorphic to the Moebius Band. Since there is no ...
67 views

### Exercise 10. Groups and Covering spaces. Lima

Let $X$ be the space obtained from the sphere $S^2$ by gluing the north pole to the south pole, let $Y=\mathbb{R}^3-S^1$, where $S^1=\left\{(x,y,0)\in\mathbb{R}^3:x^2+y^2=1\right\}$ and let $Z$ be ...
315 views

### Which surface is homeomorphism to mobius strip?

I'm a bit confused since I read many versions of this. First of all, I couldn't understand how to define homeomorphism. Intuitively, I think that if I can deform an object, without tearing it, to ...
220 views

### Paradromic rings and Mobius strip

I'm working on a project about the differences between the original Möbius strip, a strip with an additional even number of half-twists, and a strip with an additional odd number of half-twists. This ...
221 views

### What is the 'center circle' of a Mobius Band?

What is the 'center circle' of a Mobius band? The question I am working on asks me to cut (literally) a Mobius band in half 'along its center circle.' What exactly does this mean? I know the plane ...
890 views

### CW complex for Möbius strip

I was asked to find a CW complex for the Möbius strip with one 0-cell, two 1-cells, and one 2-cell. I can find a CW complex for a Möbius strip with more cells (two 0-cells, three 1-cells and a single ...
308 views

### Is there a way to prove algebraically that a Möbius strip is non-orientable?

I am doing my HL Maths coursework on non-orientability of surfaces and am trying to prove whether a möbius strip is orientable or not (of course it isn't) Is there a way to prove algebraically that a ...
194 views

### Is this a valid triangulation of Moebius strip?

This is a quick sanity check. I'd like to know if the diagram I've created is a valid triangulation of the Moebius strip or not.