Projecting Möbius Strip Edge: Learn How in 2D Plane

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SUMMARY

The discussion focuses on projecting the edge of a Möbius strip onto a two-dimensional plane. Participants emphasize that the red edge of the Möbius strip appears as a closed curve that crosses itself once, illustrating the complexity of visualizing three-dimensional objects on a flat surface. They suggest a hands-on approach by physically gluing a hollow square to create a Möbius strip, highlighting the importance of flipping edges during the process. Both the cylinder and the Möbius strip are identified as quotient spaces derived from the square, demonstrating their mathematical relationship.

PREREQUISITES
  • Understanding of Möbius strip topology
  • Familiarity with quotient spaces in mathematics
  • Basic knowledge of 2D and 3D visualization techniques
  • Experience with physical modeling or crafting techniques
NEXT STEPS
  • Explore the mathematical properties of quotient spaces
  • Learn about the topology of the Möbius strip and its applications
  • Investigate 3D modeling software for visualizing complex surfaces
  • Practice physical modeling techniques for creating topological shapes
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Mathematicians, educators, artists, and anyone interested in topology, 3D visualization, or hands-on modeling of geometric shapes.

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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