Math Is Fun Forum

Axel Johansson

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What is the 4-dimensional analogue to a mobius strip?

I'm currently researching the correlation of the area on a Mobius strip and the volume enclosed by a Klein's bottle (which is the 3-dimensional analogue of a Mobius strip) even though it is seen as an non-orientable surface, like how topologists see the sphere as a 2-dimensional surface that happens to enclose a volume.

Using the area being that of two rectangels (2LW) of length L and width W (ignoring the obnoxius differential geometry) this was a bit too easy as I quickly got the volume of a Klein's bottle to be 8LW²/pi.

To extend the topic I'm planning to generalize this into higher dimensions, and then wonder how the 4-dimensional analogy would look like, whether it would be some sort of sphere iterating over 2L to form another doughnut looking shape or if it would be anything else.

Alg Num Theory

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Registered: 2017-11-24

Posts: 693

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Re: What is the 4-dimensional analogue to a mobius strip?

I think it’s called a stereoscopic Klein bottle.

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Me, or the ugly man, whatever (3,3,6)

JohnPetterson

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Registered: 2018-04-25

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Re: What is the 4-dimensional analogue to a mobius strip?

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