Name: 17金ボトル - Numberphile (The 17-Klein Bottle - Numberphile)
Uploaded: 2021-01-14T10:16:56.000Z
Duration: 11 min 44 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

法助動詞 A2

Okay, So can you connect Klein bottles together?

命令形

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.

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?

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

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.

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.

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 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.

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

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.

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.

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.

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

Showed the still friend find Lucas Clark glass blower.

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

He makes Klein bottle off 17 individual Klein bottle units.

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17金ボトル - Numberphile (The 17-Klein Bottle - Numberphile)

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