Name: Amazing Graphs - Numberphile
Uploaded: 2020-03-27T17:45:29.000Z
Duration: 12 min 36 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Future simple

So I'm gonna be talking about graphs of sequences and I'm going to say graph.

I'm sorry I've lived in the US for so long.

Modal verbs - A2

Now, if you look at something like this, squares the squares Go one for now in 16 blah, blah, blah.

If you make a graph of them, this is a discreet sequence.

And I am as what started zero zero's term zero.

The one term is one the tooth, Miss four.

So what we get is something that looks like that if we draw a continuous curve through it, If we plotted 1000 points, the dots would add merge together and we get something that looks like that This is a parabola single dots that it looks like a continuous curve Parabola.

We're going to do more interesting things.

I'm going to show you some that you've never seen before.

But before I do that, here's another example.

The square root of an If we look at the square root of zero is 01 square root of two is 1.414 fruit to And of course, they're not whole numbers.

When I'm gonna plot in this picture is the nearest institute to the square root of end.

It's not a continuous curve anymore, because I'm rounding it off to the nearest institute.

So there are gaps like clusters are yeah, square root of 100 square, 101 squared of 102.

So that's another example of a pretty pedestrian graph.

I want to show you some more interesting sequences.

Remember that movie called Avatar The Hero?

Jake Scully gets on the banshee for the first time.

He links to it and he tries to get the banshee to fly.

Here's a sequence that reminds me of that.

What's the next time you look at the last term and in and you compare them.

They don't have a common factor on what it is.

It's the previous term event, minus one plus n plus.

What So in this case, there's no common factor.

So the next term would be one plus two plus one, which is for what goes here.

The next term is for plus three plus one.

When that happens, we divide the previous term by that common factor.

So here, the common factor this 48 divided by four is too so a event.

The rule is it's either the previous term plus n plus one.

If the greatest common divisor of a of N minus one and N is equal toe one, if they were relatively prime or it's equal to a of n minus one over G, C, D of n and A of n minus one.

If this G C D is bigger than one so that Let me let me see if I've understood it.

So there's a new common divisor there between five and to share.

So eight divided by 24 Yes, No common divisor.

Yes, we have a common divisor again, which is three.

Now we've got 10 and one so 12 there's no common divisor.

There's there's, like, 12 no common divisor there.

When we look at the graph of that, it's just wild.

It is totally random looking random array of dots until we get to term 600 something.

And at that point, Jake Sully says to the demon, Fly straight, damn it!

And from that point on, you remember in the movie, the music is chaotic, the banshee is tumbling, they're falling to the bottom of the cliff, whatever it iss.

But then suddenly the music calms down and they fly smoothly.

Situation changes when we get to a of two.

It's not until we get to term number 600 whatever it is that we first get a one at an even term.

And when that happens, let me show you what happens.

We'll have an even numbered term, which is a one.

Then there's a event now what's the next term?

Well, it's gonna be termed number two M plus one.

The next term is the sum of this, plus this plus one, which is to m plus three the next one.

So again, we add when we get four m plus six term number two m plus three ah, to impress three foreign plus six g.

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Amazing Graphs - Numberphile

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