Moebius Strips

[Skywing]

If it doesn't have two sides, how does the thickness exist?

I think you could safely call the edge of the piece of paper (or whatever thin material) that you're making the strip out of a side, because however small, it's thickness is >0.

[Soul Taker]

I don't get it either... a sphere has an outside wall and an inner wall, that's two sides.  How can you possibly have a sphere that has no inner wall?

[iago]

I don't get it either... a sphere has an outside wall and an inner wall, that's two sides.  How can you possibly have a sphere that has no inner wall?

By not making it hollow?

[Soul Taker]

How can it be a sphere, then, because it would have to have no thickness for there to be no chance of it being hollow.

[Tuberload]

You guys seem to be making this way more difficult than it is...

[Adron]

Grok, it can't be hollow because there aren't two sides between which it can be hollow.  It only has one side.

A moebius strip has two sides at every point. It just doesn't have two sides total. You can cut off a piece anywhere you like and you'll find two sides, so you can treat it as having two sides for the purpose of thickness etc.

[CupHead]

There's a difference though.  Once you cut it, it's not a Moebius strip anymore.  

[Grok]

Your definition of 'side' is flawed.

[Eibro]

I don't get it either... a sphere has an outside wall and an inner wall, that's two sides.  How can you possibly have a sphere that has no inner wall?

Cull its backfaces, then itt'l have no inner wall.

[Adron]

There's a difference though.  Once you cut it, it's not a Moebius strip anymore.  

Of course not, but you're measuring its thickness at some point, and then you can cut off a piece containing that point and you'll realize that you have no problem!

[CupHead]

But then it's not a Moebius strip anymore, so it is a problem.

[Adron]

Why would that be a problem? Do you think the thickness of part X changes because you cut it off?

Also, a theoretical moebius strip has no thickness while a "real world" moebius strip has two sides, at least.

[Grok]

Why would that be a problem? Do you think the thickness of part X changes because you cut it off?

Also, a theoretical moebius strip has no thickness while a "real world" moebius strip has two sides, at least.

That's why I asked him to confirm he was discussing a physical model, not a theoretical one.  The theoretical one has no thickness in one dimension.

[iago]

But then it's not a Moebius strip anymore, so it is a problem.

That's like saying if we take out a person's heart from his body, it's no longer a part of a person; therefore, if we study a heart that's been removed from a body, it's no longer relevant to its workings inside the body, which clearly isn't completely true.

[mejal]

Some fun to do with a mobius strip
http://www.exo.net/~pauld/activities/mobius/mobius.html