Valhalla Legends Forums Archive | General Discussion | Moebius Strips

AuthorMessageTime
CupHead
How can they exist?
October 23, 2003, 12:01 AM
warz
http://www.cut-the-knot.org/do_you_know/moebius.shtml
October 23, 2003, 12:23 AM
CupHead
Thanks, but that was useless. I know how to make one, I want to understand how it works.
October 23, 2003, 12:27 AM
Hitmen
Magic.
October 23, 2003, 12:52 AM
Yoni
[quote author=Hitmen link=board=2;threadid=3202;start=0#msg25122 date=1066870375]
Magic.
[/quote]
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!
October 23, 2003, 1:00 AM
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.
October 23, 2003, 1:09 AM
warz
The math explains it, fool. If you're looking for a visual, then follow it, it's all one side.
October 23, 2003, 3:58 AM
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.
October 23, 2003, 4:22 AM
Grok
Why don't you have a problem with a sphere, or a donut?
October 23, 2003, 4:28 AM
CupHead
Because a sphere has length, width, and depth... As does a donut. Mmm... Donut. A mobius strip doesn't.
October 23, 2003, 4:46 AM
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. :)
October 23, 2003, 5:08 AM
Adron
[quote author=CupHead link=board=2;threadid=3202;start=0#msg25162 date=1066882965]
No, fool, the math doesn't explain how a one-sided object can exist in three dimensions. I'm looking for a practical explanation.
[/quote]

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.
October 23, 2003, 10:14 AM
Grok
[quote author=CupHead link=board=2;threadid=3202;start=0#msg25169 date=1066884365]
Because a sphere has length, width, and depth... As does a donut. Mmm... Donut. A mobius strip doesn't.
[/quote]

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.
October 23, 2003, 11:31 AM
CupHead
How can an object with only one side have any thickness though?!
October 23, 2003, 1:50 PM
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.
October 23, 2003, 3:35 PM
CupHead
I am talking about the physical model, how can it have a thickness if it only has one side?
October 23, 2003, 4:30 PM
Spht
[quote author=CupHead link=board=2;threadid=3202;start=15#msg25222 date=1066926616]
I am talking about the physical model, how can it have a thickness if it only has one side?
[/quote]

The physical model doesn't have one side. Ergo,
[quote]The physical model will exist in 3 dimensions and have a positive thickness.[/quote]
October 23, 2003, 5:25 PM
CupHead
Um... Explain how it has two or more?
October 23, 2003, 5:49 PM
mynameistmp
say you had a moebius strip constructed out of a tube. originally how many sides did the tube have ? i don't see how it should be different once you construct a moebius strip. cuphead you said you don't understand how there can be one side on a 3-dimensional object, and tubes are 3 dimensional, with 1 surface to begin with, so that category shouldn't apply. if it was originally created by a tube, logic should tell you it'd result in one side. if it has no 'thickness' then it wouldn't be 3 dimensional, so that's excluded too. if you started with a rectangle, it wouldn't be a 1 sided shape, it'd have 2 sides.
October 23, 2003, 6:37 PM
CupHead
Since no one can seem to comprehend this:

[img]http://cuphead.valhallalegends.com/images/illus.gif[/img]

First of all, we can plainly see that the tube has all three dimensions, not just one surface. I have no idea where you got that from. Next to it is a piece of tape, or paper, from which to make a Moebius strip. Clearly, it has a front and a back, no? However, when fashioned into a Moebius strip, one of those sides disappears, thus losing it a dimension. Explain that.
October 23, 2003, 6:46 PM
mynameistmp
cup, we know there are 3 dimensions. when you make the tube into a torus it has more than 1 surface ?? i'm revising
October 23, 2003, 6:56 PM
CupHead
And simultaneously making no sense.
October 23, 2003, 7:01 PM
mynameistmp
i'm telling you you wouldn't use a tube or a 1 dimensional object with no 'thickness' to make a moebius strip in the first place, so forget them.
October 23, 2003, 7:03 PM
Eibro
Here's what a moebius strip, constucted of a material with no width, would look like:






October 23, 2003, 7:05 PM
Grok
He seems to have a built-in assumption that something with 1 face cannot exist in 3 dimensions, which is why I brought up a sphere, or much closer to his mobius--a donut. Both only have one face and exist in 3 dimensions.
October 23, 2003, 7:30 PM
CupHead
Grok: Assume they're hollow. They now have two surfaces. This is an object without any sides, just one continuous surface.
October 23, 2003, 7:50 PM
Grok
Aha, you just proved my point.

Why can't the mobius strip be hollow as well? The physical mobius strip has a thickness, and thus can be hollow. This is why I'm equating it to a donut.
October 23, 2003, 9:17 PM
CupHead
Grok, it can't be hollow because there aren't two sides between which it can be hollow. It only has one side.
October 23, 2003, 9:22 PM
Kp
[quote author=CupHead link=board=2;threadid=3202;start=15#msg25258 date=1066944156]
Grok, it can't be hollow because there aren't two sides between which it can be hollow. It only has one side.[/quote]I'm pretty sure that anything with a positive thickness could theoretically be hollow. :)
October 23, 2003, 9:49 PM
CupHead
If it doesn't have two sides, how does the thickness exist?
October 23, 2003, 10:21 PM
Skywing
[quote author=CupHead link=board=2;threadid=3202;start=15#msg25265 date=1066947668]
If it doesn't have two sides, how does the thickness exist?
[/quote]
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.
October 24, 2003, 4:34 AM
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?
October 24, 2003, 5:51 AM
iago
[quote author=Soul Taker link=board=2;threadid=3202;start=30#msg25317 date=1066974717]
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]

By not making it hollow?
October 24, 2003, 6:57 AM
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.
October 24, 2003, 7:36 AM
Tuberload
You guys seem to be making this way more difficult than it is...
October 24, 2003, 8:27 AM
Adron
[quote author=CupHead link=board=2;threadid=3202;start=15#msg25258 date=1066944156]
Grok, it can't be hollow because there aren't two sides between which it can be hollow. It only has one side.
[/quote]

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.
October 24, 2003, 10:07 AM
CupHead
There's a difference though. Once you cut it, it's not a Moebius strip anymore. :P
October 24, 2003, 1:10 PM
Grok
Your definition of 'side' is flawed.
October 24, 2003, 1:49 PM
Eibro
[quote author=Soul Taker link=board=2;threadid=3202;start=30#msg25317 date=1066974717]
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]Cull its backfaces, then itt'l have no inner wall.
October 24, 2003, 3:32 PM
Adron
[quote author=CupHead link=board=2;threadid=3202;start=30#msg25352 date=1067001047]
There's a difference though. Once you cut it, it's not a Moebius strip anymore. :P
[/quote]

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!
October 24, 2003, 3:38 PM
CupHead
But then it's not a Moebius strip anymore, so it is a problem.
October 24, 2003, 3:55 PM
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.
October 24, 2003, 4:01 PM
Grok
[quote author=Adron link=board=2;threadid=3202;start=30#msg25368 date=1067011260]
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]

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.
October 24, 2003, 5:17 PM
iago
[quote author=CupHead link=board=2;threadid=3202;start=30#msg25366 date=1067010936]
But then it's not a Moebius strip anymore, so it is a problem.
[/quote]

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.
October 24, 2003, 5:43 PM
mejal
Some fun to do with a mobius strip
http://www.exo.net/~pauld/activities/mobius/mobius.html
November 4, 2003, 12:13 PM

Search