Projecting Möbius Strip Edge: Learn How in 2D Plane

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Discussion Overview

The discussion revolves around the projection of the edge of a Möbius strip onto a two-dimensional plane, exploring visual representations and physical constructions related to the concept.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions how the edge of a Möbius strip can be represented in a 2D plane, referencing a video that presents the concept quickly.
  • Another participant suggests that observing the red edge of the Möbius strip in the video reveals a closed curve that crosses itself, indicating that any drawing on a flat screen is inherently a 2D projection requiring imagination to visualize in 3D.
  • A third participant proposes a physical approach to understanding the Möbius strip by gluing a hollow square in a specific manner, noting that the correct gluing leads to a Möbius strip while an incorrect method results in a cylinder, emphasizing the topological nature of these shapes as quotient spaces.

Areas of Agreement / Disagreement

Participants express different perspectives on visualizing and constructing the Möbius strip, with no clear consensus reached on the best approach to understanding its projection in 2D.

Contextual Notes

The discussion includes assumptions about visual perception and the nature of topological spaces, which may not be fully articulated or agreed upon by all participants.

YoungPhysicist
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How can the edge of a Möbius strip being projected on a 2 dimensional plane?

Precisely the ending of this video:


I just can get it since his animation goes by it so fast.
 
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how about just looking at the red edge of the mobius strip on the first page of your video. you see a closed curve that crosses itself once. i.e.anything drawn on a flat screen is already projected into 2 dimensions, it requires some visual imagination to see it as in 3 dimensions.
 
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You can actually do the gluing physically . Take a hollow square and do the needed gluing of edges , with the flip needed on the gluing for the vertices, i.e., if you do a "straightforward" gluing gives you a cylinder and one where you flip will give you the Mobius strip. To be more pedantic, both Cylinder, Mobius strip are quotient spaces of the square, i.e., spaces obtained by identifying sides of the square the right way.
 
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Thanks everyone!
 
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