Valhalla Legends Archive

How can they exist?

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

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

Magic.

Quote from: Hitmen on October 22, 2003, 07:52 PM
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!

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.

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

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

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

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

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.

Quote from: CupHead on October 22, 2003, 11:22 PM
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.

Quote from: CupHead on October 22, 2003, 11:46 PM
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.

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

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.