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#1 2018-04-18 23:26:22

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.

#2 2018-04-19 11:01:04

Alg Num Theory
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Registered: 2017-11-24
Posts: 194
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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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#3 2018-04-25 18:12:52

JohnPetterson
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Registered: 2018-04-25
Posts: 3

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

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