I'm Robert J.

我是羅伯特-J。

Lang.

蘭。

I'm a physicist and origami artist.

我是一個物理學家和摺紙藝術家。

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

而今天我被挑戰解釋摺紙和五級。

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

如果你知道一點摺紙，你可能會認為它不過是一些簡單的玩具，如千紙鶴或捕蠅器。

But origami is much more than that.

但摺紙的意義遠不止於此。

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

在浩瀚的摺紙雲中，我選擇了五個不同的層次，說明了這種藝術的多樣性。

Do you know what origami is?

你知道什麼是摺紙嗎？

Is that where you fooled?

這就是你被愚弄的地方嗎？

You fooled paper to make different animals like those?

你用紙糊弄了那些不同的動物？

Yes, in fact, it is.

是的，事實上，它是。

Have you ever done any origami before?

你以前做過摺紙嗎？

Nope.

不對。

Would you like to give it a try?

你想試一試嗎？

Sure.

當然。

Okay, so we'll do something.

好吧，那麼我們就做一些事情。

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

但我想告訴你關於摺紙的一些情況。

Most origami follows two.

大多數摺紙都遵循兩點。

I'll call them Customs.

我給他們打電話給海關。

Almost like rules.

幾乎就像規則。

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

它通常來自一個正方形，另一個是 它通常是摺疊的，沒有切割。

So these guys are folded from an uncut square.

所以這些人是由一個未切割的正方形摺疊而成的。

That's awesome.

這真是太棒了。

So you're ready?

那麼你準備好了嗎？

Okay.

好的。

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

我們要從每個日本人在幼兒園學到的模式開始。

It's it's called a crane.

它是它被稱為起重機。

Traditional origami designs over 400 years old.

有400多年曆史的傳統摺紙設計。

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

所以人們做我們要做的事情已經有400年了。

Wow.

哇。

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

讓我們把它從角到角展開對摺，然後我們再把它從另一個方向對摺。

Also a corner in the corner.

也是角落裡的一個角落。

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

但我們要把它抬起來，用兩隻手握住摺子。

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

我們要把這些角放在一起，做成一個小口袋，然後這是整個設計中最棘手的部分。

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.

所以你要把你的手指放在頂層下面，我們要嘗試讓那層沿著邊緣摺疊。

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

現在，你看到在你做這個的時候，兩邊是如何想進來的。

Yeah, it's called a petal fold.

是的，這叫花瓣摺疊。

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

它是很多摺紙設計的一部分，但它是起重機的關鍵。

Now we're ready for the magic.

現在我們已經準備好了魔法。

We're gonna hold it between thumb and forefinger.

我們要用拇指和食指夾住它。

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

伸手進去，抓住兩層之間的瘦點，也就是翅膀，我要把它滑出來。

So it pokes out at an angle.

所以它以一個角度探出頭來。

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

我們把兩個翅膀，我們把它們展開到一邊，你就做了你的第一個摺紙鶴。

Wow.

哇。

Now, this is a traditional Japanese design.

現在，這是一個傳統的日本設計。

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

但有些摺紙設計已經存在了很久，我們並不完全確定它們的起源。

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

我們要學習如何摺疊捉蝨子的工具。

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

是以，我們將從白色的一面開始，我們將把它從角到角對摺，然後展開。

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

現在我們要把四個角都折到中間的交叉點上。

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

我們將像書一樣把它折成兩半，在摺疊的一面。

We'll take one of the folded corners.

我們將採取其中一個摺疊的角落。

I'm gonna fold it up through all layers.

我要把它折起來，穿過所有層。

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.

中間有一個口袋，我們要把口袋攤開，把四個角並在一起，在這裡你有正方形的原始角。

We're gonna just pop those out.

我們要把這些東西彈出來。

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

這是最令人滿意的時刻之一，我想，是的，因為它突然改變了形狀。

I have seen this before.

我以前見過這個。

My friends, you see?

我的朋友們，你們看到了嗎？

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

是的，但我們可以用這個模型做一些別的事情。

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

我們把它放下來，按住中間的位置，然後把它從裡面彈出來，這樣就會有三個擋板升起，一個擋板保持不動。

And then it's called talking crow.

然後，這就叫說話的烏鴉。

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

因為這裡有一個小烏鴉的喙和嘴。

Wow, there's thousands of other origami designs.

哇，還有成千上萬的其他摺紙設計。

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.

但這些都是一些最早學習的人，事實上，這是我大約50年前學習的第一批摺紙設計之一。

Wow.

哇。

So what do you think of that?

那麼你怎麼看呢？

What do you think of Oregon?

你對俄勒岡州有何看法？

I think that the people that make them are talented.

我認為做這些東西的人很有天賦。

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

看到我們在這裡做的東西很難受。

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

我敢打賭，他們可以做火箭船，只是你可以用他們做這麼多。

Thanks for coming.

謝謝你的到來。

Thanks for having me.

謝謝你邀請我。

Mhm.

嗯。

Mm hmm.

嗯，嗯。

A lot of origami is animals, birds and things.

很多摺紙都是動物、鳥類和東西。

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

還有一個摺紙的分支，是，它更抽象或幾何的，叫升級。

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.

測試關係，就像大多數摺紙一樣，是由一張紙摺疊而成的，但它們做出的圖案，無論是像這樣的編織圖案還是像這樣的編織圖案。

You hold them up to the light.

你把它們舉到燈光下。

You can you can see patterns.

你可以你可以看到模式。

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

使它們變得很酷的是它們有點像貼瓷磚是。

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

看起來你可以通過裁剪小紙片和滑動它們來拼湊這個。

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

但仍有一張是他們沒有被剪掉的。

There's no cuts in these just folding.

這些東西沒有削減，只是摺疊。

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.

我們可以從較小的摺疊積木中建立這些東西，並學習如何摺疊小塊並把它們放在一起，就像這樣的瓷磚看起來是由小塊建立起來的一樣。

Can you make a fold that starts at the dot?

你能做一個從點開始的摺疊嗎？

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

它不會一直貫穿整張紙。

How about like that?

像這樣如何？

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

這些褶皺中的每一個都是像山一樣的山峰，我們把這些褶皺稱為山形褶皺。

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

但如果我把它做成另一種方式，那麼它的形狀就是這樣的。

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

我把它稱為橄欖摺紙中的山谷摺紙。

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

只是有山有谷，所以所有的褶皺都是可逆的，所以它們都是可逆的。

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

而事實證明，在每一個摺紙形狀中，折平後，要麼是山谷中的三座山。

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

或者，如果我們看的是山的背面三個山谷，它們總是相差兩個。

That's a rule of all flat Oregon.

這是所有平坦的俄勒岡州的一個規則。

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.

無論多少個摺痕都會在一個點上聚集在一起，我要給你看一個測試關係的構件，它被稱為扭曲，因為那個中心方塊，當我展開它扭曲它就會扭曲。

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

它，旋轉，如果我在同一張紙上有另一個扭曲，我可以讓這些摺痕與之相連。

These fields connect with that.

這些領域與此相連。

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

如果我在這上面還有一個，我就可以把這三個都做出來。

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.

如果我有一個正方形數組，所有的摺痕都排成一排，我可以做出越來越大的數組，就像這些，因為這些只是非常大的扭曲，在這種情況下是一個八邊形而不是正方形。

But they're arranged in rows and columns.

但它們是按行和列排列的。

And let's just try going along.

而我們就試著走下去吧。

Yeah, mhm.

是的，嗯。

Alright, there is our desolation with squares and hexagons.

好了，這就是我們用正方形和六邊形的荒廢。

So you have now designed unfolded your first origami desolation.

所以你現在已經設計展開了你的第一個摺紙惆悵。

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.

也許你可以看到，僅僅利用這種堆砌瓷磚和小積木的想法，你就可以使測試關係變得像你想擁有的學校一樣大和複雜。

Yeah.

是的。

So what do you think now of origami and escalations?

那麼你現在對摺紙和升級有什麼看法？

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

摺紙，我想，是指用紙折出任何東西，從三個D的東西到像，呃，扁平的東西，一般來說。

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

而我認為摺紙是把簡單的東西變成複雜的東西。

And it's all about patterns.

而這一切都與模式有關。

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

這是一個偉大的定義，所以這裡有一隻蜻蜓，他有六條腿。

Four wings.

四個翅膀。

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

這裡有一隻有八條腿的蜘蛛，有腿的螞蟻，這些就像仙鶴一樣是由一個未切割的正方形摺疊而成的。

What to figure out how to do that?

怎樣才能想出辦法來呢？

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

我們需要學習一下什麼才是重點。

So let's come back to the crane.

是以，讓我們回到起重機的問題上來。

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

你大概可以看出，廣場的四角最後是這樣的點。

That's a corner.

那是一個角落。

Four corners, the square, four points.

四個角，正方形，四個點。

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

你會如何用這張紙做一個點？

I'm thinking of like a paper airplane.

我想的是像紙飛機一樣。

Yeah, exactly.

是的，沒錯。

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

實際上，你已經發現了一些很整潔的東西，因為你提出了你的觀點，而不是從一個角落裡。

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

所以你已經發現了其中一個關鍵的見解。

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

螞蟻的任何一個瓣，任何一個點Leg都佔據了紙張的一個圓形區域。

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

這裡是我們的邊界 為了從一個邊緣上提出你的觀點，你用那麼多的紙和形狀。

It's almost a circle.

這幾乎是一個圓。

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

如果我們拿著起重機，我們會看到在起重機的圖案中是否可以看到圓圈。

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

這裡是起重機的圖案，這裡是機翼的邊界。

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?

而這裡是另一隻翅膀，克朗有四個圓圈，但實際上有一點驚喜，因為這個呢？

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

有一個1/5的圓圈就像這樣，但它的起重機確實有1/5的襟翼在裡面。

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

讓我們把它和翅膀重新摺疊起來 嗯，是的，有。

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

還有一個點，這個點就是我們鶴立雞群的第五圈。

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.

為了做到這一點，我們使用了一種叫做圓圈包裝的新技術，其中設計師的所有長條特徵都用圓圈表示。

So each leg becomes a circle.

是以，每條腿都成為一個圓。

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.

每個翅膀都變成了一個圓，而那些可以又大又厚的東西，如頭部或腹部可以在中間點。

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

現在我們有了如何設計模式的基本想法。

We just count the number of legs we want.

我們只是計算我們想要的腿的數量。

We want a spider.

我們想要一隻蜘蛛。

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

如果它有，比方說，八條腿，它也有一個腹部。

That's another point.

這是另一個觀點。

It's got a heads.

它有一個頭。

Maybe that's 10 points.

也許這就是10分。

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

如果我們找到一個由10個圓組成的排列，我們應該可以把它折成蜘蛛。

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.

所以在這本書中，摺紙昆蟲到 這是我的書之一，有一些圖案，這是其中一個飛翔的瓢蟲。

And in fact, it is exactly this flying ladybug.

而事實上，它正是這隻飛翔的瓢蟲。

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.

我們已經在這裡得到了圓圈的摺痕模式，你現在可能能夠看到哪些圓圈最終成為哪些部分。

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

知道最大的特徵，如翅膀，將是最大的圓圈。

Smaller points will be smaller circles.

較小的點將是較小的圓圈。

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

這麼多想法，這可能是，嗯，腿和天線可能要小一點。

Yeah, that's right.

是的，這就對了。

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

這看起來像背面，因為一路有一堆圓圈，像這裡。

Exactly.

正是如此。

And then and then the wings.

然後是然後是翅膀。

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

你有四個大翅膀，你可以在兩端看到。

And then I guess that you got it.

然後我想，你得到了它。

So you are ready to design origami?

那麼你準備好設計摺紙了嗎？

Awesome.

棒極了。

Yeah.

是的。

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.

現在全世界的摺紙藝術家都在用這樣的想法來設計，不僅是昆蟲，還有動物和鳥類以及各種東西，我認為這些東西複雜得令人難以置信，而且很逼真，但最重要的是，很美。

Wow, that's so impressive.

哇，這真是令人印象深刻。

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.

我想我在三年級的時候學會了如何製作這種紙鶴，但我想我從來沒有展開過，沒有真正看到它是怎麼來的。

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.

是以，現在所有的東西都被抽成了圓圈，它使這些超級複雜的昆蟲和動物，一切都顯得如此簡單。

So that's so cool.

所以這太酷了。

Thank you so much for telling me about this.

非常感謝你告訴我這件事。

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.

每當航天器的某個部分的形狀有點像紙，也就是說它又大又平，我們就可以使用摺紙中的摺疊機制來使它變小。

Telescopes.

望遠鏡。

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.

太陽射線 它們需要被裝入火箭，升空，但當它們升入太空時，會以一種非常可控的確定性方式膨脹。

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

這些是很多很多摺紙可展開形狀的構件。

It's called a degree four Vertex.

它被稱為四級頂點。

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

它是線的數量，所以在這種情況下，我們用實線來表示山。

We use dash lines for valley.

我們用破折號線表示谷底。

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

我們要把它折起來，用這些來說明摺紙機制的一些重要特性。

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

在機制研究中，考慮到剛性是很重要的。

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.

是以，我們要做的是幫助模擬剛性，就是把這些矩形，我們要把它們折來折去，使它們變得僵硬和剛性。

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

好的，所以這就是所謂的單自由度機制。

You have one degree of freedom.

你有一個自由度。

I can choose this foal.

我可以選擇這匹馬。

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

然後，如果這些是完全剛性的，其他每一個摺疊角度都是完全確定的。

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.

這裡的一個關鍵行為是，在這裡的小角度上，相同模仿的兩個褶皺和相反模仿的褶皺的移動速度差不多。

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

但隨著我們越來越接近90度，我們發現它們的移動速度非常不同。

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

然後在運動結束時，發生了相反的情況。

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

這個幾乎是摺疊的，但這個經歷了更大的運動，所以相對速度不同。

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.

是以，當我們開始把這樣的旋渦粘在一起時，如果它們是單獨的單自由度，那麼我們就可以製造非常大的機制，打開和關閉，但只有一個自由度。

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

是以，這些是一種叫做鏡子的圖案的例子，或者當你把它們拉長時，它們是相當大的，好嗎？

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.

它們可以摺疊成平面，一個幾乎與此完全相同的圖案被用於1995年飛行的日本任務的太陽能電池組。

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.

是以，你就像，緊湊地飛起來，然後一旦你到了那裡，就像，有某種像，機動的機制，但你只需要它在一個摺疊。

Yeah, so typically, what?

是的，所以通常，什麼？