Valhalla Legends Archive

Quote from: CupHead on October 23, 2003, 05:21 PM
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.

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?

Quote from: Soul Taker on October 24, 2003, 12:51 AM
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?

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.

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

Quote from: CupHead on October 23, 2003, 04:22 PM
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.

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

Your definition of 'side' is flawed.

Quote from: Soul Taker on October 24, 2003, 12:51 AM
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.

Quote from: CupHead on October 24, 2003, 08:10 AM
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!

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

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.

Quote from: Adron on October 24, 2003, 11:01 AM
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.

Quote from: CupHead on October 24, 2003, 10:55 AM
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.

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