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Probably not. I just took the first word that came to mind. I would likely use path so that I directly have a parameterization to work with - just in case. It avoids reediting.martinbn said:
Undergrad What is the 4D Equivalent of a Möbius Strip or Klein Bottle?
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The discussion explores the concept of higher-dimensional analogs of the Möbius strip and Klein bottle, suggesting that if the Möbius strip represents 2D and the Klein bottle represents 3D, then a 4D equivalent could be the real projective space or a generalized Klein bottle. Participants clarify that both the Möbius strip and Klein bottle are non-orientable surfaces, with the Klein bottle being a two-dimensional manifold that cannot be embedded in three-dimensional space but can in four dimensions. They also mention that certain three-dimensional manifolds can be constructed from cubes by identifying pairs of faces, leading to various generalizations of the Klein bottle. The conversation emphasizes the complexity of embedding these manifolds in higher dimensions, with some requiring five dimensions for proper representation. Overall, the thread highlights the intricate relationships between dimensions and the properties of these unique mathematical surfaces.
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