Is a Mobius Strip Truly a 2D Object in a 3D Space?

In summary, a Mobius strip is a two-dimensional object that is embedded in a three-dimensional space. It is a standard example of vector bundles or manifolds and can be defined without this embedding. It is a non-simply connected surface, meaning it only has one side and can be continuously traveled around and return to the starting point. It also has the characteristic of mirroring objects when traveling around it. Mobius strips are often used as a way to visualize and understand higher dimensions and their compacting into various shapes. They can also have topological charges and produce interesting effects when combined or cut.
  • #36
LightningInAJar said:
But with the twist it pushes into 3D space so requires the 3rd coordinate?
We say it is a 2D object embedded in a 3D space. Mathematicians seldom care about how the strip is embedded so they just use the two coordinates.
 

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