Name: 平面圖 - Numberphile (Planar Graphs - Numberphile)
Uploaded: 2021-01-14T10:16:06.000Z
Duration: 16 min 24 s
Description: 【看影片學英語】數萬部 YouTube 影片，搭配英漢字典即點即查，輕鬆掌握單字發音與用法，長久累積看電影不必再看字幕。

today is gonna be about plainer graphs, graphs that can be embedded in the plane.

Okay, so what's the graph from what's a plane?

I'll tell you all about that photograph consists of a bunch of foreign skeptical verses, and then some pairs of Earth's is air joined by a line that tickle and edge.

And like this and Sampras averts is don't have anything between them.

This is also Graf called the house you actually call that helps we actually go over the house way.

When I was school, a graft may had, like an X and A Y access and the line and things like that.

Completely unrelated is just an unfortunate, uh, overloading, overworked lately, different concept.

And then the question is were asking your drawer.

So this is a plain piece of paper is a plane.

And the question is which grafts can you draw in the plane s O that ages don't intersect.

So what does me natures don't understand Don't intersect where they should, for example, in these graphs, the sage and they said the Intersect over here, but you meant it.

There intersect over here because they have a common rex over here.

But for example, if I make these drawing so it's all the verses are 1234 The age of the 123 These age and their page the Intersect.

They just intersect because I drew it like this.

So graphics plainer if you can join in the plane or in a piece of paper in such a way that to wages on the Intersect, where you intended them to intersect only in the second it works.

Professor, if you draw a graph and edges intersect, does that mean it's not a graph or it's invalid?

This is a graph in this photograph it's called an abstract graph, and then you can ask about We'll talk about a plane and embedding autograph and what that man said that you've thrown it like this.

I'm betting this is only illegal if what you're after, it's plain.

It's probably possibly good for some applications, like if you want to in a V L a psych component or something which I don't know anything about.

But it's just it's just another appropriate and math.

We'll think of an object to think of a property and then we say, Do all the soldiers have this property?

Though some of the Soviets has this property, can you tell if you have this property?

Can you characterize when you have this property so being plainer, it's a property some graphs have and sound graphs don't have.

And I actually haven't told you what plane it means yet.

I think I told you what a plane they're embedding is, But I haven't told you what the plane a graph is so graphics plainer if it has a plane there embedded, for example.

These guys also has a plan embedding name to this one.

This graph, no matter how hard you tried, does not have a plan.

That is exactly that is a direct witness.

These only different from bed by one drinks.

But these you could it actually in bed in the plane.

Because what you do issue number, the virtues that you believe me, it's a embedding.

And we care about which pairs of verses are adjacent.

Wanted Jason to do 22332 1/4 address into the mall.

So these abstract graph is the same as that abstract stuff.

This is plain embedding this is not a plane.

Edges have to be straight like, Could you have kept these voter sees in the same places and, like, drawn curved lines around the place toe as well?

Or I just don't have to be stating the terms that said that anything you can embed with curved ages, you can embed with straight ages.

Uh, so you're asking me, Could I leave these four verses in place and just, uh, make that just yet?

So what I would do is so I could make this completely s symmetric ugly drawing or this beautiful join?

But on the other hand, you know, they say, you can see how to get it, which I think has a lot of value.

It's a theorem that any plane a graph that you can draw with curved edges.

You could also have demonstrated that That's really cool.

I learned a Stearman the right time in my life.

I was in high school when I heard about it.

So I am, in fact, as amazed by the stream as one should be.

I haven't become jaded by the time I heard of it.

But you can't do any trickery with that like you did there.

That one's trick there is one more week and doing a trickery, and in fact, that's usually how interaction to plan a graph start.

So you have three houses and three utilities.

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平面圖 - Numberphile (Planar Graphs - Numberphile)

incredible

bunch

mess

property