Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

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

Axel Johansson
Guest

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
Member
Registered: 2017-11-24
Posts: 194
Website

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

I think it’s called a stereoscopic Klein bottle.

Offline

#3 2018-04-25 18:12:52

JohnPetterson
Banned
Registered: 2018-04-25
Posts: 3

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

Thanx for sharing such useful post keep it up smile advertising link removed

Offline

Board footer

Powered by FluxBB