Name: Impossible Squares - Numberphile
Uploaded: 2020-04-05T03:02:07.000Z
Duration: 13 min 25 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...

Modal verbs - A2

I would like I've got some dotty paper on the brown paper here so I could draw stuff on these dots.

To-infinitive

I'm gonna draw a square, but I'd like to tell me how big a square.

So it is possible to draw a square of size 16 and I want to say size.

What other squares are possible to draw on this grid on the rule is I gotta use the dots and straight lines between dots.

I don't think this is a trick question, but could you suggest another square size?

I could draw what you could do, like a two by two.

Every four before going to 16 obvious ones.

Do you see the soul of numbers we're getting here?

You always were getting square numbers because you're drawing squares.

The naming is a good thing here so I could draw 149 We didn't do that.

It's not a surprise that you can draw a square number.

Or could it could one drawer square on this grid using the same rules during the dots.

That's no square diagnose or something or slightly squares that are allowed as long as we stick to the dots.

I'm gonna start with this dot I won't go along the vertical or horizontal.

I can go a certain amount down to send along.

So four down here and on Wrangel go across to cross, too.

If that's the side of the square, I better do this one sort of four along.

So it was definitely a square, and you asked me to go sort of four down too long, which means all of the triangles like that so there's two.

There's four, so maybe we call it the 24 square.

And once it's area, I don't think this is much less obvious to me.

You could chop it into bits and work out the air of the bits.

Or you could look at the area of the big square, which I think is six by six.

Let's call it half times two times four, which means it's one times four, which means four in here, all together, four times for 16.

Get so we've drawn squares on the grid that are not just the square.

Do one can we do to Turns out to is really easy.

So this is area two and you do the same trick with the outside square.

Realize that area four and you got to Anyway, can you do three?

This is suddenly no obvious, Andi you start drawing stuff and ends up being very hard to draw three, at least even if it's possible.

It's not easy to do, and I think you can then convince yourself quite quickly that it can't be done.

Committee five Let's try it can't be a vertical horizontal one.

So we're gonna have to go a bit of a slanty thing.

And if I go to down on one along, so the square's gonna look, let's give myself some space.

That's sort of diagonal, which means he's like a a two and a one sort of vector s o.

The other side was going to that that as long as I do a two and a one on each vector, I'm pretty sure that's five.

Then I enjoy the thing around it, which is now nine, because it's three by three and these triangles have calculated Let's do it.

This is 21 So the area off one, the whole thing's nine the four triangles give me four, so this is very fine.

The problem is, even if you allow slanty squares, which was your genius idea at the door to the square numbers some you can d'oh!

Indy five, maybe 20 to 10 Be county three.

The question I want to investigate in this video, that is, which squares candy drawer?

And is there a short cut of finding what the areas that you could get?

So 20 took us a little bit of calculation with them.

Trying was the five took us a bit, but I did.

I used to mother notations There's this to four notation that when we're 20 and the 21 notation number five and if we use the same notation, this could be kind of like 40 notation because for every side you go along for and down zero, I could write down all the list of notation I could do.

I could do 11121314 and I could just check all the list and I could find pretty easily just by search of all the numbers and realize there's some missings.

Six is missing, seven is missing, 11 is missing and already we're secrets and like and all prime.

One of them's perfect like what's going on and I really don't think is obvious before we go any further, though.

What would be nice if first of all, we could find a shortcut for instead of home to draw thing and counting trying course.

How can I just write down the notation for the sort of slanty nous and get straight to the area?

I've seen this active activity done with sort of a nine year old school students, and they're busy drawing squares and calculated, and they were having a lovely time It Suddenly there's this deep glimpse of math so that, like that goes way beyond what they're ready for.

But what they already for is is finding a court collectivism area.

A slanty square's gonna fit inside another square.

If I say that this distance is a and this one is B, then we've kind of got this.

This is like our A B notation that we had.

Then how big is the square in the middle?

And it's not too bad I can work out the side of the big square.

Thes triangles turn up all the way around, so the whole square is a plus B squared.

We can take away the triangles from that, and we'll get the area of this central bit.

I think the triangle is relatively obvious is a B.

Subtitles ListPlay Video

Impossible Squares - Numberphile

stuff

sort

obvious

multiple