Name: パスカルの三角形 - Numberphile (Pascal's Triangle - Numberphile)
Uploaded: 2021-01-14T10:15:44.000Z
Duration: 12 min 33 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：

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one and then we add whatever is to the left

of it - so it's neighbor here is 0 and we just

Alright cool now I have two ones in this row

and the zero to its right we make another one.

in particular like problems where "If I have

triangle is really like "childlike adding

in particular let's say i have four things

I want to only choose one of them - there are

I can choose that one, I can choose that one

And it turns out Pascal's triangle says if I go down to the

fourth row and - where it like this is the

0th row - and I choose one thing so I move

(Brady Haran) So if i told you to choose two circles-

You notice that the sides are always ones

1 + 0,  1 plus 0. And this is just gonna keep

But then we get to this row right and we have

I have 0 1 2 3 4 5 so i can define this row

pattern looks less fun right. I have One, a Three

10 and 6 is 4 so it turns out this pattern is

something else one that might be tempted to

So this is 1. One plus 1 is 2. One plus 2 plus 1 is 4.

You'll notice that some point I just stopped adding

because we can actually rewrite everything over here as

the powers of 2. So the sum of the rows of

Pascal's triangle is two -  like if I'm on

the Nth row and I call the first one row zero then

Let's just read these as numbers let's not add

them let's not treat them as anything else

The next row is a hundred and twenty one. The next row is thirteen thrity-one. Then  we get

So ,right now these are actually the powers of 11 too

So this next row looks pretty frightening

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パスカルの三角形 - Numberphile (Pascal's Triangle - Numberphile)

bunch

pattern

imagine

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