Name: アメージング・グラフII（スター・ウォーズを含む） - Numberphile (Amazing Graphs II (including Star Wars) - Numberphile)
Uploaded: 2021-01-14T10:15:14.000Z
Duration: 10 min 49 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：

it is cool, balanced Turnberry, and what you do is you write your number in base three and then your place all the tools by minus ones.

命令形

One it's fixed to in base three just says to Andi, The rulers replace all the tools by minus ones, so this is now minus 13 Internally, it's one not so it doesn't change.

Four is 11 intern ary, and it doesn't change.

Still, four five is one to which becomes one comma minus one.

Now one common minus one means 13 minus one.

So it's 26 is 20 which becomes minus 10 which is minus three.

Let me remind you were writing numbers and base three.

So it's minus one comma zero sub three, which means minus three plus zero zero on the ones in the one's position that suits my history.

Seven is to one, which becomes minus +11 So that's minus three plus one, which is minus two and so on.

And if you do this, you get all the insurgents both positive and negative.

It's a way, if in a concise way of the numerator ng all the all the insurgents.

And if you look at the graph, it looks like this It looks like Star Wars.

They're all those star destroyers here here, And that graph will eventually as expands out floor every single interview, negative and positive here little they're just keeps coming.

So now the sequences you take, n you write it in base 10 and you subtract the product of the non zero digits.

One product is one Subtract we get 02030 Very boring up 290 because the number of minus the product of its digits is zero.

If there's only one digit Okay, 10 10 has one non seven digit one.

Its product so subtracted We get 9 11 has the product is one.

Look at the product of the non zero digits and subtract it from the number 10.

14 is 10 again and well, let's jump forward by the time we get up to 25.

So we subtract 10 from 25 when we get 15 so it's drastically changed.

I call it mysterious because to a gardener this looks very like wisteria purple flowers you see in the trees.

It's like the group gets bigger, but it never droops further than well.

You're not subtracting very much because you're looking at the product of the digits, and that's much less than what you started with since the digits rule nine or less.

So once you start getting interesting numbers like, you know, 4692.

Yeah, four times, six times nine times two is whatever it is, but it's not very big, so it's not.

It doesn't drew very far from what you started with something like some pretty big groups there.

Well, yes, they had a lot of big digits like that.

So this is the forest fire and rule is that we put down the Mexican graphically earliest sequence, meaning you always pick the smallest numbers.

That's easiest way we start off when we have a choice.

So so far we don't have anything to worry about, so I can pick a one.

Okay, I can put another one because it's not a big deal.

The rule says you may not have three terms that air in an arithmetic progression, meaning the difference between here and here is the same as the difference between here and here.

So a of I plus Jay Miner save I must not equal a of I Plus two J minus ev I plus J.

I would like to put a one here because that's the smallest legal move.

But then the difference between then these three terms if we did that, we'd have a one and a one and a one, and they will be equally spaced.

They jump I zero each time equally spaced numbers with a constant difference between them.

It's not allowed, so we go to the next time.

There's nothing wrong with putting a two there.

Well, I could put a one there because there's no conflicts.

And therefore I must, because there are no three ones that are evenly spaced.

Can I put it to We can't put a one because we'd have 111 And that would be a violation of the rule.

Constant increment of 03 equally space terms.

Well, I think it's gonna be a problem if we have one.

Because 1 to 4 to seven, we would have a one jump of three on a one again jump of three.

111 at three terms which share equally spaced.

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アメージング・グラフII（スター・ウォーズを含む） - Numberphile (Amazing Graphs II (including Star Wars) - Numberphile)

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subtle

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