Could a piece of tubing be twisted into a Möbius strip?

No, because the Möbius strip is 2-D. The Möbius strip is produced by giving a half twist to a plane, the strip, and connecting the ends of the plane.
The strip inside the twisted tube would be 2-D, but the tube remains 3-D.

Yes, you’re picturing it right. I can’t think of any practical applications either, but I agree that it’s a fun idea.

It does seem like it would work with a slightly flattened tube. Maybe a tiny butter churn.

It would be Möbius-like, In that the surface was would twist, but as mentioned it’s not a Möbius, since it still has two distinct surfaces. A Möbius-like 3-D object already exists (...kinda), it’s called a Klein Bottle. Kinda hard to make properly in physical space, though.

A mathematician named Klein
Thought the Möbius band was divine.
Said he: “If you glue
The edges of two,
You’ll get a weird bottle like mine,

Leo Moser

Interestingly, the Möbius strip can be embedded in three-dimensional Euclidean space; the Klein bottle cannot.

I just made a drawing (with a cutout section) for visualization purposes.

Real life Mobius strips are a great solution for industrial belts or belts for car engines. The wear is even and lengthens teh life of teh belt.

I feel like this would be an interesting roller-coaster feature.
The loop-de-loop, the corkscrew, the Möbius.

No. To have a Mobius strip, the item must have two opposite sides that will become one. With tubing, you are dealing with, in effect a circle where the outside (or the inside) is only one side and will continue to be so after the Mobius is attempted.

Thanks @thorninmud for the picture.

I figured that I could not possibly be the first person to think of this. I found a YouTube video with a square tube. I could not find anything with an object inside, but surely someone must have thought of it.

But, the tube has to be flattened, right?
Otherwise you just have a tube circle?

That is a good question. I don’t think it should make a difference. With a circle you can control just how much twisting that you do.

It’s interesting that only guys answered this question. I know what a Mobius strip is but have trouble picturing what you’re all talking about. Curious and curiouser…..

@LostInParadise @thorninmud I could make a couple with the 3D printer: hollow or solid. It is a “flash forge”, dual filament machine printing in ABS or PLA plastic. It takes only STL files in millimeters. I just need the drawing and would be happy to send it to you (free) if you keep it a reasonable size and weight ~2 inches .
I have access to a really nice high end machine but the costs are outrageous. It can make it out of almost any material: nylon, steel, gold.

@LuckyGuy You are a lucky guy to have a printer like that. I can supply a STL file if @LostInParadise is interested.

@LuckyGuy, @thorninmud, Thanks.
How much would this cost? I would be glad to compensate for material and labor, but anything much over $15 is not really worth it, as neat as this would be as a desk ornament.

@LostInParadise The thing with a Mobius strip is that it only has one side. But you knew that, right?? A circle, or piece of tubing, square or round, has 2 sides that will still be 2 sides when you complete your connection of the two ends.

Sorry guys. Your money is no good here. It is my gift to both of you: @LostinParadise for thinking it up and @thorninmud for drawing it.
@thorninmud I’ll PM you with an email address. Please keep the OD to 50mm.

I picture this like a chocolate coating over a Mobius strip.

@LuckyGuy Now you’re tawking!

@janbb You heard the accent, didn’t you.
“I got it. I got it.”

@thorninmud Sent.

I hate to be a wet blanket, but isn’t a piece of flexible tubing (air line?) and either a short peg or hollow tube all that’s needed?

If I had a fish tank or oxygen tank, all I’d need would be a chunk of pencil (to shove the ends together on) or a piece of ink pen (to slide the ends into) and a foot of air line?

@ibstubro That is true. You could do it with a pencil and it would not look like anything special. But, imagine a flattened tube with a rectangular prism inside that is free to move around the tube. Paint the top half of the prism red and the bottom half blue. When the prism makes one loop around the tube the red and blue sides will reverse. Cool!

Here is a fanciful idea. I don’t know if it could be done, but it is fun to think about. Imagine the tube as a railroad tunnel. The passenger train that runs on it has an additional set of wheels to connect to the portion of the track that is above it. When the train makes a complete loop it turns upside down. Maybe we can make the seats swivel in such a way that the passengers remain right side up. If the train is a double decker, the upper and lower sections will reverse.

@thorninmud File received and forwarded to the guy for review.

@LostInParadise Your description is exactly how I imagined it! There would be tracks on the roof and the floor and the train would be held monorail style from the top and bottom. At some point in its travel the train would be horizontal with the upper and lower deck side by side. That would be peak tensile loading foro the monorail mounts.
Hey @thorninmud If you can draw it up we can make one out of nylon. At $3 per gram it won’t cost much more than $200 million. :-)

@LuckyGuy Sure, and at 10 minutes per day, it shouldn’t take me more than 200 million days to draw it.

@thorninmud Great! It’s nice when timing and resources line up. I’ll put it on his schedule.

My goal was answering the question:
“Could a piece of tubing be twisted into a Möbius strip?”
as expediently as possible?
And testing the rotating interior object theory?

Reply from the print reviewer:

“I just looked at the mobius ring. I think his printer would goof on the underside undercut. If printed on a side – opening down, one edge is quite undercut and approaches the table at a very small angle. My shells must be printed solid with the base shown in this picture.

It did print the planetary gear set shown too, with nice double helical gear teeth.
-A”
@thorninmud Did you make the drawing of the mobius tube with the end open, or closed? I think we want it closed. Also I think the printer will work best if the strip it is attached to a base that we can cut off after printing. Can you add one?

@LuckyGuy The file I sent is a closed loop, but it’s also a solid. I can redo it as a hollow form if needed. And I’ll add a base.

@thorninmud Anybody can make a solid. Having it hollow is the cool part! That is the magic – even if you can’t see it.

@LuckyGuy OK, new version sent, hollow and on a base.

Got it and forwarded. Wall thickness might be too thin. I am confirming now.

@thorninmud and @LostInParadise You probably thought I’d forgotten about this – but you’d be wrong! Life got busy.
I got the first prototype two weeks ago It was supposed to have a moveable shuttle inside and an inspection port so you could see the shuttle change orientation every time it went by. Cool. Well, upon receipt the shuttle was stuck inside and not moveable. There was supposed to be 0.5 mm of clearance but the loose powder stuck to the sides. I went in with a tube of canned air and managed to blow out much. then used water, then air, then water, etc… then a flex tube to push against the shuttle and – it started to move!
Eventually I got it to go around with the help of my air compressor blowing on one side of the inspection port. I kept at it. and now it spins around at about 4 times per second when I hit it with an 80psi air stream. It needs to be worked in.
I am redesigning it to have holes all around the outside and increasing the clearance to 0.75mm. That should do it.
When (not if) it work I will send to you.

Thanks for the update

@thorninmud I just sent you a photo of V4.0 . The shuttle is inside but you can’t see it. You can only hear it moving around in the tube. Technically that is really interesting and almost magical – but not very good visually. V5.0 will have holes in the tube wall so you can see inside. That’s the one I will send to you two.
I need addresses.where I can sent them. If you want to stay anon I will gladly send it to an office, PO box, or anywhere that accepts a package.

@LostInParadise I need your email address so I can send you the photo too.

Update….
With high pressure air and a pinpoint nozzle I managed to make the shuttle orbit inside the tube faster than 10 Hz. I ran it for about 1000–1500 cycles. That really smoothed the parts but wore the color off the shuttle. One side was blue: the other white. Now there is only a little bit of blue showing. Oh well. At least is moves smoothly.
Look at the photo.

Very cool, thanks! I see you had to make it a bit bigger.

@thorninmud Yep! You noticed. It needed to be bigger so the shuttle would be a reasonable size. I can now put my fingers into it and hold it like brass knuckles.
I’m glad you like it!

Guys, I just sent you an email. The designer working on Ver5.0 made a discovery!

Is it black hole from the Large Hadron Collider? ? ? ?

@Tropical_Willie We made the discovery when we were revving the shuttle up to high speed.
When it was orbiting in the tube at between 600 rpm and 1200 rpm, and spinning around its major axis as well, we noticed it stayed in the same orientation as it passed the inspection window. The color remained white instead of pale blue. That was a surprise. We expected it to alternate between the 2 colors: blue and white . We discovered a mistake in the drawing. Three (allegedly) competent designers and engineers, me included, all missed an error in the tube orientation.
Fortunately we figured it out before making too many.