Name: 四色地図の定理 - Numberphile (The Four Color Map Theorem - Numberphile)
Uploaded: 2021-01-14T10:15:25.000Z
Duration: 14 min 18 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：

命令形

So let's talk about the four color theorem!

so the statement is, every map can be colored using four colors,

such that two neighboring countries are different colors.

In other words I'm saying there are no maps that need five colors.

and you'd think more complicated maps would need more colors,

but apparently all maps can be done with just four colors or better.

So this problem was unsolved for a long time.

although the method they used to solve it was a little controversial at the time,

but has had a large effect on mathematics today.

So the story of how this problem came around is kind of cute.

Apparently there was a guy who was trying to color in the counties of Britain.

I don't know why he was trying to do that, but he was,

and he suspected he could do it using four colors.

And he mentioned it to his brother, and his brother was a Maths student.

And his brother mentioned it to his lecturer who was a man called Augustus De Morgan.

He's a famous mathematician, and, well, it was De Morgan who spread this problem around.

we either need to show that every map can be done with four colors or better,

or we just need to find one example that needs five colors.

And if you try it with maps, it does work.

If you try it with the map of the world, you can color it with four colors.

If you try it with the map of the United States, you can do it with four colors.

You can try any real map, you can do it with four colors.

I mean you can get this problem to children, right, you want to keep them quiet.

Maybe if I can invent a weird, complicated map,

So that's what you start to do -- doesn't look like any sort of real-life map.

So we got this map, and now we're going to color it in.

So let's start with the middle; I think orange.

Next country has to be a different color, so I'm using the purple here.

so this is all fairly simple -- I can't use purple, I can't use orange, because they're touching --

Next one, uh, what do you want, what do you want, Brady?

[Brady] Well, we can't use blue or orange... [Dr. Grime] Mm.

[Dr. Grime] Ah, wise. That is a wise choice.

Why not? Let's not go to the expense of using a fourth color.

[Dr. Grime] And we can use blue again for that one, excellent.

That might put us in a good position when we do the next country.

we can't use blue, we can't use purple; what should we use?

[Brady] We can use orange again. [Dr. Grime] We can use orange, why not?

Uh, do you wanna use the orange on the opposite one?

[Dr. Grime] We do need -- we have to go to the fourth color, do we?

Yeah, yeah, yep, purple, blue and orange are being used;

this does have to go into the fourth color.

I've got pink here. On the opposite side, it's the same, obviously; I'll use pink over here.

It looks like we had to use four colors for that.

Here's another important map. I'm gonna make

countries, but if we try and color it in,

the orange in the middle again, purple up here.

can't be orange. That means it's blue and this

purple; it can't be blue; so I'm forced to

bit. Let's say I took this map again -- I'll

draw it here. Same map. Instead of coloring in

That'll just get the same idea won't it? I don't

border. Right, I'll just connect them with

the same color?" So it kind of boils down

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四色地図の定理 - Numberphile (The Four Color Map Theorem - Numberphile)

scenario

apparently

controversial

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