I'm Robert J.

Lang.

I'm a physicist and origami artist.

And today I've been challenged to explain origami and five levels.

If you know a little origami, you might think it's nothing more than simple toys like cranes or cootie catchers.

But origami is much more than that.

Out of the vast cloud of origami possibilities, I've chosen five different levels that illustrate the diversity of this art.

Do you know what origami is?

Is that where you fooled?

You fooled paper to make different animals like those?

Yes, in fact, it is.

Have you ever done any origami before?

Nope.

Would you like to give it a try?

Sure.

Okay, so we'll do something.

But I want to tell you a little bit about origami.

Most origami follows two.

I'll call them Customs.

Almost like rules.

It's usually from a square, and the other is It's usually folded with no cuts.

So these guys are folded from an uncut square.

That's awesome.

So you're ready?

Okay.

We're gonna start with a model that every Japanese person learns in kindergarten.

It's it's called a crane.

Traditional origami designs over 400 years old.

So people have been doing what we're about to do for 400 years.

Wow.

Let's fold it in half from corner to corner unfolded and then we'll fold it in half the other direction.

Also a corner in the corner.

But we're gonna lift it up, and we're gonna hold the fold with both hands.

We're gonna bring these corners together, making a little pocket, and then this is the trickiest part of this whole design.

So you're gonna put your finger underneath the top layer, and we're gonna try to make that layer fold right along the edge.

Now, you see how the sides kind of want to come in as you're doing that.

Yeah, it's called a petal fold.

It's a part of a lot of origami designs, but it's key to the crane.

Now we're ready for the magic.

We're gonna hold it between thumb and forefinger.

Reach inside, grab the skinny point that's between the two layers, which are the wings, and I'm gonna slide it out.

So it pokes out at an angle.

We'll take the two wings, we spread them out to the side, and you have made your first origami crane.

Wow.

Now, this is a traditional Japanese design.

But there are origami designs that have been around so long We're not entirely sure where they're originated.

We're gonna learn how to fold a cootie catcher.

So we'll start with the white side up and we're going to fold it in half from corner to corner and unfold.

And now we're gonna fold all four corners to the crossing point in the center.

We'll fold it in half like a book on the folded side.

We'll take one of the folded corners.

I'm gonna fold it up through all layers.

There's a pocket in the middle We're gonna spread the pocket and bring all four corners together where you have original corners of the square.

We're gonna just pop those out.

This is one of the most satisfying moments, I think, Yeah, because it suddenly changes shape.

I have seen this before.

My friends, you see?

Yeah, but there's something else we can do with this model.

We set it down and push on the middle, Then pop it inside out So that three flaps come up and one stays down.

And then it's called talking crow.

Because here's a little crow's beak and mouth.

Wow, there's thousands of other origami designs.

But these are some of the first people learn, and this was, in fact, one of the first origami designs I learned some 50 years ago.

Wow.

So what do you think of that?

What do you think of Oregon?

I think that the people that make them are talented.

It's hard seeing the stuff that we've made here.

I bet that they could do rocket ships just so much that you can do with them.

Thanks for coming.

Thanks for having me.

Mhm.

Mm hmm.

A lot of origami is animals, birds and things.

There's also a branch of origami that is, it's more abstract or geometric called escalations.

Test relations, like most origami, are folded from a single sheet of paper, but they make patterns like whether it's woven patterns like that are woven patterns like this.

You hold them up to the light.

You can you can see patterns.

The thing that makes them cool is they're sort of like tiling is.

It looks like you could put this together by cutting little pieces of paper and sliding them together.

But there's still one sheet that they weren't cut.

There's no cuts in these just folding.

We can build these up from smaller building blocks of folds and learn how to fold little pieces and put them together in the same way that tiling like this looks like it's built up of little pieces.

Can you make a fold that starts at the dot?

It doesn't run all the way across the paper.

How about like that?

Each of these folds is peaked like a mountain, and we call these mountain folds.

But if I made it the other way, then it's shaped this way.

I'll call it a valley Fold in olive origami.

There's just mountains and valleys, so all the folds are reversible, so they're all reversible.

And it turns out that in every origami shape that folds flat, it's going to be either three mountains in the valley.

Or, if we're looking at the backside three valleys in the mountain, they always differ by two.

That's a rule of all flat Oregon.

No matter how many folds come together at a point, and I'm gonna show you a building block of test relations, it's called a twist because that center square, as I unfold it twist it twists.

It, rotates if I had another twist in the same sheet of paper, I can make these folds connect with that.

These fields connect with that.

And if I had another one up here, I can make all three.

And if I had a square array and all the folds lined up, I can make bigger and bigger arrays like these because these are just very large twists in this case is it's an octagon rather than a square.

But they're arranged in rows and columns.

And let's just try going along.

Yeah, mhm.

Alright, there is our desolation with squares and hexagons.

So you have now designed unfolded your first origami desolation.

And perhaps you can see how just using this idea of building up tiles and small building blocks, you could make test relations as big and complex as you want to have a school.

Yeah.

So what do you think now of origami and escalations?

Origami, I think, is the folding of paper to make anything in general from three D things to like, uh, flat things.

And I think origami is about turning simple things into complex things.

And it's all about patterns.

That is a great definition So here's a dragon fly and he's got six legs.

Four wings.

Here's a spider with eight legs, ants with legs, and these just like the crane are folded from a single uncut square.

What to figure out how to do that?

We need to learn a little bit about what makes a point.

So let's come back to the crane.

You can probably tell that the corners of the square ended up this points.

That's a corner.

Four corners, the square, four points.

How would you make one point out of this sheet of paper?

I'm thinking of like a paper airplane.

Yeah, exactly.

Actually, you've discovered something pretty neat because you made your point, not from a corner.

So you've already discovered one of the key insights.

Any flap, any point Leg of the ant takes up a circular region of paper.

Here's our boundary To make your point from an edge, you use that much paper and the shape.

It's almost a circle.

If we take the crane, we'll see if the circles are visible in the crane pattern.

And here's the crane pattern, and here's a boundary of the wing.

And here's the other wing, the krona has four circles, but actually there's a little bit of a surprise, because what about this?

There's 1/5 circle just like that, but it does the crane have 1/5 flap in it.

Let's refold it and the wings up Well, yes, there is.

There's another point, and that point is the fifth circle of our crane.

And to do that, we use a new technique called circle packing, in which all of the long features of the designer represented by circles.

So each leg becomes a circle.

Each wing becomes a circle, and things that can be big and thick, like the head or the abdomen can be points in the middle.

Now we have the basic idea of how to design pattern.

We just count the number of legs we want.

We want a spider.

If it's got, let's say, eight legs, it's also got an abdomen.

That's another point.

It's got a heads.

Maybe that's 10 points.

If we find an arrangement of 10 circles, we should be able to fold that into the spider.

So in this book, origami insects to It's one of my books and has some patterns, and this is one of them for flying ladybug.

And in fact, it is exactly this flying ladybug.

We've got the crease pattern here in the circles, and you might now be able to see which circles end up as which parts.

Knowing that the largest features, like the wings, are going to be the largest circles.

Smaller points will be smaller circles.

So many thoughts, which might be, well, the legs and the antenna would probably have to be the smaller ones.

Yeah, that's right.

This looks like the back because there's a bunch of circles all the way down, like here.

Exactly.

And then and then the wings.

You've got four big wings, which you can see on the ends there.

And then I guess that you got it.

So you are ready to design origami?

Awesome.

Yeah.

Origami artists all around the world now use ideas like this to design not just insects, but animals and birds and all sorts of things that are, I think, unbelievably complex and realistic, but most importantly, beautiful.

Wow, that's so impressive.

I think I learned how to make one of these paper cranes when I was in third grade, but I guess I never unfolded it to actually see where it was coming from.

And so now that it's all broken up into circles, it makes these super complicated insects and animals, and everything seems so much simpler.

So that's so cool.

Thank you so much for telling me about this.

Whenever there's a part of a spacecraft that has shaped somewhat like paper, meaning it's big and flat, we can use folding mechanisms from origami to make it smaller.

Telescopes.

Solar rays They need to be packed into a rocket, go up but then expand in a very controlled deterministic way when they get up in the space.

These are the building blocks of many, many origami deployable shapes.

It's called a degree four Vertex.

It's the number of lines, So in this case, we use solid lines for mountain.

We use dash lines for valley.

We're gonna fold it and use these to to illustrate some important properties of origami mechanisms.

It's important in the study of mechanisms to take into account the rigidity.

So what we're gonna do to help simulate rigidity is to take these rectangles, and we're going to fold them over and over so that they just become stiff and rigid.

Okay, so this is what's called a single degree of freedom mechanism.

You have one degree of freedom.

I can choose this foal.

And then if these are perfectly rigid, every other fold angle is fully determined.

One of the key behaviors here is that with the smaller angles up here, the two folds that are the same parody and the folds that are of opposite parody move at about the same rate.

But with this as we're getting closer to 90 degrees, we find they move at very different rates.

And then at the end of the motion, the opposite happens.

This one is almost folded, but this one goes through a much larger motion, so the relative speeds differ.

So when we start sticking together vortices like this, if they're individually single degree of freedom, then we can make very large mechanisms that open and close, but with just one degree of freedom.

So these are examples of a pattern called the mirror, or when you stretch them out, they're pretty big, okay?

And they fold flat and a pattern almost exactly like this Was used for a solar array for a Japanese mission that flew in 1995.

So then you, like, fly it up compactly, and then once you get up there, there's like, some sort of like, motorized mechanism, but you only need it on one fold.

Yeah, so typically, what?

The mechanism will run from corner to corner to diagonally to opposite corners, because then you can stretch it out that way.

Notice some differences between the one you have and the one I have, and how this one sort of opens out almost evenly.

But this one opens out more one way and then the other.

Yeah, what sort of angle would you want so that they open at the same rate?