Name: Möbius Knots and Roller Coasters - Numberphile
Uploaded: 2020-03-30T07:35:20.000Z
Duration: 5 min 43 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

And we did that in Breckenridge, Colorado.

So here is a Mobius pant that makes three twists okay by itself.

You know, we don't care about the shape the Mobi spent by itself is really no different to a mathematician than the rubber band.

It's just a loop, Okay, we're not looking at the cross section, and whether it's twisted or not, it's just we're looking at the center line off the not that defines the knot.

But once you take the Mobi span and he split it down the middle, it becomes a not now.

Not because now, if you had thes stands being nice and soft, you could move them around and they would be interlinked in exactly the same way as this compass structure.

If it's only single, I twisted it will simply open up in a loop that's twice the size and actually has a full twist in it.

If the Moby Span is even more twisted, like five times, you may get this other not that we had labeled as five someone or something like that.

We started out this a trefoil knot now, and so here he's roughly triple knot.

And then we split this trifle not down the middle because it happens in this trifle not to be off a Mobius structure.

Let me back up a little bit and show you two different profiles.

I kind of call them, like, you know, trefoil standing on its own two feet because they were carefully designed so that I can actually so standing up, they're not gonna topple over.

Well, I'm claiming one of them is a mobile span, and the other one is not, Let's figure out, you know, whether this one is twisted.

So I'm starting on the side of it's a camera up on the low pier on them, running my fingers slowly down here.

I'm staying here on the upper side of that foot.

I'm coming up here on I'm back where I started it.

Irene and I could paint the other one rant and everything would be fine.

But now let's compare that to the other movie spent.

If I'm starting here again on your side, I'm moving down here.

I'm getting to the bottom off this foot on the bottom off this highly curved little thing.

I'm going through the middle, staying at the bottom here, staying at the bottom side, coming around.

Begin the bottom of this foot now coming up the back side.

And so basically, I'm coming after the backside and I've gotten to the other side if I continue again sliding down here, being on the upper side, sliding over on the upper side here, coming back and I'm coming back to where I started.

But I had to go around the loop twice, and in that process I would have painted everything green right.

And there's no way I can paint one of the other side without the two colors running it too.

This is the idea off a Mobius trifle Not.

And then we took a slightly different shape off again.

You can see this looks roughly like a, um, a trifle not, except it started out with a cross section that was more or less, you know, rectangular originally.

But then we carved out the middle part to make essentially a split and because it's a Moby spanned when I do this, I get a Not that it's not really divided.

If you start on this side off the big lope and you go around the whole Roller Coast, by the time you come the first time back up on the mountain, you're actually are on the other side.

And then you have to go once through Maur through the roller coaster until you come back to where you started.

So it's just one long string, you know, essentially tied together and vile when it was still fused without the gap in the middle, it was a trifle.

It's a much more complicated not how many crossings does this thing have.

Actually, not that easy to see, but I was amazed a day Miss Sarai.

It was like a seven year old kit, and I show them that and within seconds he said 12th and he realized wherever we had a crossing in our trifle not We now had split that we now get four crossings.

We have this situation and so indeed he is.

Right now we have three times four crossings.

So by the time they're kind of looking through the not table, you're already you very far down.

There were other thousands of different knots, and that's just one of them roller coasters.

I'm pretty sure that some of them are because, I mean, that makes kind of fun.

You know, you wanna many of them has of these, like, figure eight configuration ago, sometimes run Lupin, then to go through the figure eight.

By the time you go off a couple of times through the middle of this figure eight, it is very likely that the things are not that.

But you can never be quite sure there's some very complicated looking knots that you can find on the Internet.

Like when you look for something like difficult a knot or difficult.

This is a real not, but actually It's not experimental part off the innate apology.

So the field is called the innate apology with study geometry, anthropology off circular, the molecules or linear the molecules that locally behavior circles.

 Now you're gonna take this lace put under that loop. 