Undergrad Projecting Möbius Strip Edge: Learn How in 2D Plane

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The discussion focuses on how the edge of a Möbius strip can be visualized when projected onto a two-dimensional plane. It highlights that any drawing on a flat screen is inherently a 2D projection, requiring imagination to perceive it in three dimensions. Participants suggest physically creating a Möbius strip by gluing edges of a hollow square, emphasizing the importance of flipping the vertices during the process. The conversation also notes that both the cylinder and the Möbius strip are quotient spaces derived from the square by appropriately identifying its sides. Understanding these concepts enhances the comprehension of the Möbius strip's unique properties in a 2D context.
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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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