Name: アメージンググラフIII - Numberphile (Amazing Graphs III - Numberphile)
Uploaded: 2021-01-14T10:17:07.000Z
Duration: 8 min 40 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：

A famous gutting and mathematician from the 19th century.

It's one of the bigger entries in the only I s Let me give you the simplest definition.

The 1st 2 terms are one and one for the next two terms.

I copy the one in the one and put there some in the middle, so the sequence now begins.

I copy the previous line, and in between I put the someone Plus two is +31 plus two is three, so we have now shown you a triangle.

It's It's a very common number, theoretically.

I copied the previous line, and in between them, I write some of the two terms about that, just as you said, just like Pascal's triangle.

If I admit the last one, it has the property that if you look a ratios of successive terms, fractions one over 11 over to two over 11 over 3 1/3 insured three over to its one and 1/2 to over three.

We get all the fractions in their lowest terms.

It's a way of a numerator ng the fractions.

After a while, we get seven seventeenth's get 100 and one over 103 and so on.

We get all of them little ones and big ones, and they're always reduced.

112 1323 Just read it like you do with Pascal's trying off.

If you plot it, you get something that looks pretty nice.

Like I'm on a sketching the facades of some cathedrals.

And the interesting thing is that we don't know if this exists or not.

We don't know if Schrodinger's cat is alive or dead, Fibonacci says.

The day of N is equal to a of hen minus one plus Ava and minus to some of the two previous times off status sequences.

Event is a N minus a van minus one plus a of n minus A of N minus two.

Can you show me an example how that works?

Just like the standard naive for Ballouchy version.

You go back one step, and you go back two steps, right?

You go back one step and went back two steps and Adam up this one off.

Status que sequence you look at the previous term.

But that's how many terms you have to go back to get the thing you're adding.

So going back one step gives us a one going back.

One step because of that one gives us one.

We get a one, we go two steps back and we get a one and that says, Go back one step and we get it too.

One plus two 03 So that one So so that one told us.

But one step from our starting point again.

Yeah, And whatever you see on do your finger, you add it to the other one.

So for the fifth term, Yeah, that's a three.

Okay, so then we go back to numbers, which says, Go back to numbers to there.

Number 6 to 33 Bank 123 So give us a two, too.

1232 Again before and once more to make sure I've got a four steps.

Well, now, if we're lucky, we can always do that.

But suppose there was a number here which was too big, and that that would say, Oh, you've got to go all the way back here where it's not defined.

It hasn't happened yet, but we can't prove that it never happens.

If you look at the graph, this is 10,000 terms.

Then we'd run into trouble if we had a term that was a big A Zen, because this line has slope 1/2.

Well, even though there is some little dots trying to escape some little particles trying to get away, they have to get it all the way up to here or something before they would kill it.

We've checked Roman Piss computer 10 to the 10th terms.

Never, never a problem, but not proven now proven.

Here's a picture of 100 million terms that I got from Douglas Hofstadter, who invented the sequence and you can see beautiful ribbon like structure, but no proof it could die at any moment.

Slightly different rule, but uneven Maur striking picture.

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アメージンググラフIII - Numberphile (Amazing Graphs III - Numberphile)

subtle

term

negative

structure