And if so, what do you get?

Well, now take a Mobius loop, right?

I give up half twist.

Get a Mobius loop.

What if I give it another half twist?

Turns out that's not a Mobius loop.

It's two sided.

Give it yet another half twist.

It becomes a Mobius loop.

Probably the most famous movie IST loop has 3/2 twists to it.

It's the recycle sign, and you can see there's 12 3/2 twist to it.

That's a Mobius loop, just like that's a Mobius loop.

To be a Mobius loop, you have to be able to walk on all one side without crossing it.

EJ.

Yep.

Okay.

Got that 10 my fingers are blue from having tried to put blue dye into a Klein ball.

Ignore that they'll wash off in the next two or three weeks so I can make a three twist Mobius loop.

Can I do the same thing with a client bottle?

What if I take a Klein bottle and add another Klein bottle?

Tow it.

Oh, I can't go over the glass shop.

Get a scissors.

Cut that there.

But that there.

Get another one and build this.

Is this a client bottle?

It's too.

Klein bottle for welded together.

Oh, it's get up pen.

Okay, let's start over here and write the letter A and the letter B.

Well, it's third it, eh?

Going along here?

Oh, I can't keep going.

I'm on the inside of this party.

Still on the inside, Still on the inside, Still on the inside.

They'll come out over here and come back to a so I can go from a all the way back.

Aye, but I never get to the letter b meaning that this side here, the A side is different from the B side.

Be an air on different sides.

So, Cliff, someone watching might be thinking Although I could just run my finger directly from a to bay.

But you're you're cheating if you go like this and go bonk like that.

No, we're talking about we're talking about, ah, mathematical thing like this.

Where?

Where?

Where?

My glass blower had actually caught a hole here so that you could go be zip through it, go around the inside.

Not this is as is a figment of our figment.

of our three dimensional universe.

Of that, seven more that one that self intersection does.

That self intersection doesn't come from the outside here.

Now, you're on the inside of this way on the outside of this in your back there.

So this turns out to have two sides and hold their This is home to more fit to a tourist.

Okay, got that.

What if I add another one to this?

I'll go from here to here.

Here's three flying bottles arranged.

Well, let's try the same experiment.

All right, A over here.

Be and see.

Okay.

Triple Klein bottle.

Go from a who?

Over here.

No, I'm on the inside of the baby.

Still in the inside.

I come out here.

No, I'm on the outside of C.

Okay.

Outside of sea.

Go back here.

Outside.

Outside.

Outside.

Outside.

Oh, book.

I end up on the inside of a mmm around the inside of eight.

I'm now right behind here.

So without lifting the pen from the surface of the class, I've gone from the outside from the outside, Over here, over to the inside.

This is one sided.

Let's keep going.

And still on the inside of this one on a millimeter away from here is wearing talk still in the inside story inside Come around here.

I've hit the outside of hit Be hot Diggety Ah, cool.

Now I come around and I'm on the outside Think through there now I'm on the inside of this I have reached the other side off the sea surface I stand that other side Come out here I am back to where I started I've covered the entire surface and aunt could walk on the entire surface of this and make this real Ignoring places were you can't get through So this is a client bottle.

It's one sided.

There's no edge.

At no point is there sharp edge that the caterpillar crawling the surface ever got cut on.

You could paint the whole thing by pouring paint over one side.

And that's right.

If I if I hired a painter, they could paint the whole thing with one side in one color piece of cake.

Works like gangbusters.

Showed the still friend find Lucas Clark glass blower.

He thought about it for a while.

He said, Why?

You're trying to tell me that any even number of client bottles linked together as a tourist.

Any odd number 135 is a Cline.

Dion.

Listen, yeah, that makes sense.

He makes Klein bottle off 17 individual Klein bottle units.

Brady, check this out.

Check this out.

Each of these each little unit.

There's a client bobble, and if you count him, you'll count 17 Klein bottles.

But wait, wait to show how nutty Lucas is.

Each Klein bottle in this linked set of 17 Klein bottles twists just enough so that it's a Mobius loop off Klein bottles.

He actually made a mistake, but I'll ignore it.

Don't tell anyone that he sort of flipped one around.

This is a Mobius ring of Klein bottles, just a CZ.

You could say that a Klein bottle is the connected.

Some off to Mobius Loops here connected some of 17 Klein bottles as a Mobius ring.

Oh, my move, You're amazing.

Was hard to make.

Does it hurt to make?

Oh, why?

Like why knock on the door that glass up?

I won't say that everybody runs and hides but multiple Klein bottle manufacturing, such as this or three external Klein bottles.

Or suppose instead of making three Klein bottle by cutting these together and hang them together like this.

Suppose I removed this section.

It put a smaller Klein bottle right there.

Cut this and build it in there.

And then over here I go take this part out, cut that out and put it in an even smaller Klein bottle in.

So I have three Klein bottles which are internally linked rather than externally linked.

Well, in that case, I'll end up with something.

Yeah, that looks like this.

Okay, this is home.

You morph IQ to this Klein bottle, both of which are homey amore fick to unordinary regular playing bottle.

Like this guy here.

This is three internally linked Klein bottles.

So this hole here is map.

Well is really the same as this hole here.

And that leads outward through this tube coming back to the next one in, goes to here, comes up and around out here, that tube goes to another Klein bottle, which is completely linked up here and comes out this way to the outside, which comes back to here.

Dillard's Here's a triple plain bottle, which has the same properties.

Is this triple Klein bottle.

Which internal which in turn have the same properties if this guy which also have the same properties as this Klein bottle.

All of which is to say, if you're looking for zero volume, one sided are three immersed, not embedded Klein bottles, huh?

There's plenty to explore with glass Brady.

If you're going to show, feel ex Klein behind a Klein bottle, there's Moebius, framed by a Mobius loop You've already broken at 1 75 I've broken it once, and Adams and George George didn't it over it.

Adam mentioned in glass, laughed at me and said, I'll fix it for you Just this once.

He patched up just so I'm not gonna I treated with delicacy.

Enjoy.

It's a wrong the idea of making ah 17 unit Klein bottle into a Mobius.

Lucas Clark.

Over here, Lucas is a complete nut.

Loose.

This is astonishing.

You're gonna have to take a picture and send this to my friend.