Really mean.

Like, you get to have, like, a little companion.

Why would he do that?

Was to encourage you to eat because he liked You know what?

I'm actually allergic to oranges as well.

So it would be all nice and fun until I was sick.

Did something.

But the mathematical idea appealing a two dimensional object into the surface of a sphere has stuck with you.

Thank with May have lost my place.

Now get when we head like leg.

Need another arm.

The reason I wanted to shade it was because I was always something a little bit annoying about the orange man.

It's fine.

It's legs coming off now.

Wait, wait.

Magic should sit up.

Okay.

Now it kind of works.

That kind of works, right?

It kind of works.

So they're gay.

He's sort of that.

I took his leg off.

If you well, wherever he's kind of cool like this little Lawrence guy is more like a starfish.

Really.

Here's one handed right now.

Are you really okay?

Early one was a bit better.

My practice one was a bit better, and this is a fresher and nothing.

That's my problem.

I just realized that you are.

I know exactly what the problem is.

They even though you've got this kind of quite fun little guy you can never get him to sit flat on the desk can never quite get him to, like, lay perfectly flat.

Especially not without really deforming the orange Bill.

And there's a reason for that.

And the reason is something called the gassy in curvature.

Now, gassing curvature is a number that describes how curving surfaces and it's made up of two things multiply together.

One is how the surface curves in one direction.

The second number is how it curves in the perpendicular direction.

You multiply those two together to get the gas in character.

No matter how you bend a surface gassing curvature will always stay the same.

So here, with an orange, it's positive in that direction, positive in that direction.

So whatever you do to the surface of an orange, it always has to have some kind of a bend away from you.

You actually want your orange man to lie flat two dimensional surface, which has zero gassy curvature.

So there's no way that two positive numbers can ever multiply together to make zero.

And that doesn't really matter so much when you're talking about orange peels or the Orangemen.

But it does matter when you really want to make the surface of a sphere life flat on a two dimensional surface like when you're trying to make a map of that.

Okay, so one option that goes, if you wanted to effectively peel the surface of the earth to make a map is tiu cut up all sorts of slips like this unfurled, um, kind of like this and then squish it as little as possible.

So I am still you will end up with these kind of defamation.

Tze the skin deforming as you squish it down, especially the ends.

They're not really gonna match together very well, but you've kind of got a sort of flat shape that came from the surface of your sphere and that really is the idea behind you'd Hummel sign projection, which sometimes gets nicknamed the orange peel projection in kind of see why it does a good job.

It's certainly flat, but you have to squish quite a lot of this to get it into the right place.

So this map here doesn't preserve direction very well.

On also is not particularly useful for navigating.

I mean, you're kind of coming off hand.

There's this massive gaps, just not very nice, not particularly.

So this is a very squished at the top.

So if you kind of look at the top here, the shape of the of the land of the coast doesn't quite match the shape that you get up here.

But also actually, if you sort of imagine folding this round in tow three dimensions and stitching it back together, you wouldn't get a spherical shape.

So you can kind of see how things have been literally squish down effectively.

This isn't gonna work very well.

Is that the world's?

There are a few different options here, but none of them are going to get you completely around the problem of transforming the surface ever sphere into a fractal dimensional space.

So one option you could say OK, well around the equator, thes squares of last year's multitude of quite square, and that's quite nice.

Maybe you want to try and keep that.

So when you go up the top, maybe you say Okay, well, why don't we deformed these areas so that they're always nice, neat rectangle by the time it gets to beats paper.

For that, you end up with something that looks like the equity rectangular project in here, which is certainly the world on its, you know, successfully on two dimensions.

But the problem with this one is that direction goes all over the place here.

So if you take one of the ones that near the North Pole, this line here is actually really tiny when it is on the globe.

So if you want to get from one corner of this to the other, you'll end up going in like this very weird path.

It's not very good for navigation, so that leads to the map that probably most of us know which is made by.

Instead of taking big sheets of paper, I'm forming a cylinder around your glow.

Now you can imagine that you've got light on the inside of this globe.

That's right in the center and shining outwards and then if you traced shadow of the land on the papers, it was wrapped in a cylinder around you would end up with Mercator projection.

This is what Google Maps uses, and it doesn't really good job, especially keeping the shape of the country's quite nicely on also in preserving directions.

This is really good for navigation.

If you want to get from London to Brazil, you can just head in a straight line and what will be the shortest way to get there.

But you know you're going to get there.

So that's kind of why the Mercator projection is quite handy.

The only problem about Mercator because you're using a cylinder things are gonna be distorted at the polls much more than their distorted at the equator, and as a result, the area of different landmasses ends up being completely, completely mucked up, completely skewed.

So if you look on the Maketa man at Greenland in Africa, look roughly the same size.

But when you look on the globe, Africa is absolutely bloody massive, and Greenland is teeny tiny, so excuse your perceptions or together another one is that Australia sitting just below the equator.

The topic is anyone.

E is actually the same size of the entire ity of bloody Europe on the real globe, but I think it just ends up.

You get bit distorted when you look at things on the McKay tomorrow.

There's still a problem here, right?

McKay does not.

Perfect.

There's always gonna be a problem on the spot.

Something isn't isn't a paper that I've liked for a long time is this paper here is called orange peels and frazzle into girls.

And essentially, in this paper they showed.

If you peel an orange in a spiral and then lay it flat on a table, two very nice things happen.

First off, as your number of loops in your spiral tends to infinity, the shape that it makes on the table tends to ula.

Spiral is very, very beautiful.

Neat mathematical shape.

Whether curvature changes linearly as you move along, it really just a lovely idea.

Also, the amount that your orange peel has too deformed to lie flat on the table tends to zero as your number off loops in your spiral tends to ability.

So I think we've missed trick here because I think that this is what map should look like I think that we should have.

We should prioritize mathematical beauty over geographical practicality.

What is it doing?

The other maps aren't doing well.

It's not gonna be deformed.

All of the other maps have deformed in some way.

And also see us spiral.

Brainy.

One more do you want?

So this is a you a spiral map.

A new way of Matt.

Can we do this?

I don't see why.

No, I reckon.

Cut this on up and see what happens.

Like like the way you would peel an orange, right?

Like if you were doing a spiral in the north, they start the top and then just wind your way down.

I'm just gonna deal on the earth.

Some of the top.

When the way down.

Why not?

You didn't.

Okay?

Did you do a risk assessment?

Ready?

I can get it.

Hit it.

Hit it.

That each one of you hit the seam through Russia.

Okay, so, ideally, you'd be doing this really, really fine.

That you're I mean, we've only go.

Benny got this room booked for another hour.

His bags turn down.

The world's really big, you know, cutting through red light we'll see.

Brady will see.

It's literally paradise on a ruined It completely does is unbelievable.

No, we didn't go.

Okay?

I don't get it.

I think I need Thio.

Just gave it for that.

I missed it.

Technically, I missed it.

Advice of me.

Do you want to?

You know what?

You're going to preserve it.

I mean that.

Let me take you now.

We should both have bad things.

Do.

They're doing really well on this thing.

Which move it, I'll tell you what room.

Big enough.

Okay, so you have to remember I have done a finite number of spirals on the rial.

Ula Matt protection, as it is now gonna be called, would have an in flight number.

It's worth it, though.

Brady, for the mathematical beauty that will unfold.

Can you do the other spiral?

I think when I went to your domestic just a thistle is not how much my life living that writes that second at roughly the same size as the other one.

Yeah.

Yeah.

You like it?

Almost.

Actually, this'll kind of works.

This kind of works as a map.

I think people could get used to this.

You bring on the bridge of your ship.

It doesn't mean, you know, if you're in sort of Paris and you want to go to Vienna, you're fine.

But if you want to go north, Thio north to London, he do.

You have to do it in my lap of the globe, but, you know, simple sacrifice.

So if you had end loops on your globes with one of these Barrows is was like one of this defamation reduces, like one over n squared.

So you know you're gaining the Maur loops you have, the more you gain, I think, as a map projection, you know, this is mathematically beautiful.

If geographically and practical get solution, check out these problems and questions.

All of them involved the Earth, maps, globes.

They're questions that I really hope you get your head around this stuff in today's video, and all of them are on brilliant dot org's who were the supporter of today's video.

Their brilliance full of quizzes and courses and puzzles on all sorts of subjects from mathematics and science.

But don't feel intimidated.

Don't think they're trying to test you or make you feel dumb.

This is all about changing the way you think, making you smarter and better attacking problems.

But if you don't know the answer, that's fine.

There's no judgment.

In fact, even go and read a whole bunch of people talking about how they would have attacked the problem.

Real mind broadening stuff that got a brilliant dot org's slash number file to check out all the stuff.

There's loads of stuff on the site for free, but if you want to sign up for the premium membership, you get 20% off.

If you slash number five now, thanks to a brilliant for well, trying to make the world a smaller place.

Hey, and speaking of planet Earth, why don't you check out Hannah's latest book?

It's called Hello World.

I'll include a link down in the show.

Notes, along with a brilliant link actually did work out All right.

Hey, it's fun.

It's fun.