Moebius Strips

[CupHead]

How can they exist?

[warz]

http://www.cut-the-knot.org/do_you_know/moebius.shtml

[CupHead]

Thanks, but that was useless.  I know how to make one, I want to understand how it works.

[Hitmen]

Magic.

[Yoni]

Magic.

You misspelled "Math".

In an effort to make this post not as useless I will add a link explaining some of this math. Check out the gears animated gif!

[CupHead]

I already saw that, it didn't explain much.  I'm looking for an explanation of how a three-dimensional one-sided object can exist.

[warz]

The math explains it, fool. If you're looking for a visual, then follow it, it's all one side.

[CupHead]

No, fool, the math doesn't explain how a one-sided object can exist in three dimensions.  I'm looking for a practical explanation.

[Grok]

Why don't you have a problem with a sphere, or a donut?

[CupHead]

Because a sphere has length, width, and depth...  As does a donut.  Mmm...  Donut.  A mobius strip doesn't.

[Raven]

A mobius strip doesn't necessarily exist; it should exist, by theory. The three-dimensional plane is often denoted by a coordinate plane of an intersecting x, y, and z-axis, with the z being the "through-dimension" axis. Now, let's say that when you plot the mobius strip, it's coords (in (x,y,z)) would include points such as (0,0,8), (0,0,4), (0,0,-2), and (0,0,-8). This way, the mobius shape itself can actually be flat in every dimension it exists in, yet still span through multiple dimensions. This is all theoretical, ofcourse. Obviously I may be wrong, but I think that's the way it works. Hopefully that helped atleast a bit.

[Adron]

No, fool, the math doesn't explain how a one-sided object can exist in three dimensions.  I'm looking for a practical explanation.

Isn't it obvious how it exists after you make yourself one?

And yes, a mobius strip has length and width and depth depending on what coordinate system you pick.

[Grok]

Because a sphere has length, width, and depth...  As does a donut.  Mmm...  Donut.  A mobius strip doesn't.

A donut is no different from a mobius strip in dimensions, other than their thicknesses.  They both share the same general shape in one axis, and differing thicknesses along the angular path (circumference).

Unless you're talking about a non-real mobius strip with a 0-thickness?  If so, that's little different from a 2-dimensional plane that you twist a little bit to make it appear 3-dimensional.  But a mobius strip just gets twisted pi radians.

[CupHead]

How can an object with only one side have any thickness though?!

[Grok]

There's your problem, you're the one defining it to have only one side and no thickness.  So I ask you again, are you talking about a physical model of a mobius strip, or the theoretical one?

The physical model will exist in 3 dimensions and have a positive thickness.
The theoretical one will exist in three dimensions and have zero thickness.

The physical model will be characteristically the same as a donut.