Name: 三角形超級英雄 - 數字愛好者 (Superhero Triangles - Numberphile)
Uploaded: 2021-01-14T10:15:32.000Z
Duration: 16 min 38 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。

These are special triangles and they're called hero triangles.

You're like that, Hiromi In triangles on these are particular types of hero triangles.

Hero Triangle is a triangle that has introduced sites holder besides, on an interject area.

Okay, so it's just something that mathematicians like to play with.

You should think of these a lot like perfect numbers and things like that.

It's just something that mathematicians like that fun with.

Even now, we're still coming up with new things about them.

The superhero trying These are superhero triangles.

I'm now giving you permission to put Clickbait thumbnails on this video.

Get Captain America over here Are Can't believe it's superhero triangles.

So the idea is they've got into decides on So this has sides 5 12 and 13 which is called a Pythagorean triangle as well.

But this is why I wanted to point out Look at the perimeter of the perimeter is adding up the three sides.

If you work out the area where it's half the base times the height of you, remember formula for an area of a triangle, which will be 30 as well.

That's what these five triangles have in common.

So if I do the next one, you could see this one's a right angle triangle as well.

Perimeters 24 area is 24 that's a look of these.

Yeah, these last three and drawing out are not right angle triangles.

We look at the perimeter or perimeter 42 area for two.

You everyone's favorites on the last one is really long.

The way that they kind of refer back to itself a perfect numbers when you look at the factors of the number and it adds up to itself and it reminds me of that the perimeter and the area of the same on, even though there are an infinity off possible triangles we could have with inter decides into your areas.

These are the only five that have the same perimeter in the same area, so there is five and five only.

Presumably you can upsides the same fire that I's a good point.

But the problem with that is, if we talk, say this triangle, if we double it, then we would double the perimeter and the area gets multiplied by four.

So when you double the perimeter areas mortified by four so even coat, including scaled up versions of triangles at this is the five the only five we confined.

So let me give it, give you some facts about this.

It's just one of those things mathematicians study.

So these are facts about the hero nian triangles, which means they have into decides and into your area.

So they are named after a mathematician from way back 2000 years ago, hero of Alexandria.

We saw that we can do it with a Pythagorean triangle.

And there are infinitely many of these on their quite easy to make.

I mean, the simplest is the 345 triangle Perimeter 12 on the area, half the base times the height is six.

But any Pythagorean triangle would work as another example 17 15 8 would work as well.

So he's got an interview Perimeter, which I think is 40 on the area is, ah, interview as well.

That's gonna be guaranteed to be in interview.

So they're heroes, but not superhero guaranteed.

Every pie factory and triangle is going to have this property because you're gonna have an integer perimeter on.

Yet you're guaranteed to have into your area as well.

What I mean is your guarantee, cause it's half the base times the height.

It means you are a guarantee that one of the's sides is an even the sound of all those infinite Pythagorean triangles.

Only two of them have this property where the area is the same as the perimeter on then the other three are not right angle triangle.

If you wanted an equilateral triangle like this recites all the same length, whatever that is, I'm afraid that's never going tohave an integer area.

So you can't do it without collateral triangles.

Wells, Could we do water about a nice sauce?

Perimeter ISS 16 on the area is going to be 12.

So we've got injured your perimeter into jet area.

I don't have you noticed it was a bit of a cheat because if I drop a vertical line here, what it is is actually too right Angle triangle stuck together.

It's actually a 543 right angle triangle stuck together.

So I'm afraid Yes, you can do I saw city strangles although they are a bit of a cheat, So can we make triangles that are not a bit of a cheat?

Okay, so we'll get will go a bit more, General.

This is one of our hero triangles, but I've cheated again because you can drop a vertical line.

You can split into two right angle triangles.

Are there any triangles that aren't just made out of Pythagorean like angle triangles?

And so you can do triangles that aren't cheats?

So here's a triangle with a perimeter off 64 on an area of 72 on that cannot be broken up into two right angle triangles.

That a pie factory and you drop her vertical line here where we know what.

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三角形超級英雄 - 數字愛好者 (Superhero Triangles - Numberphile)

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