My talk is "Flapping Birds and Space Telescopes." And you would think that should have nothing to do with one another, but I hope by the end of these 18 minutes, you'll see a little bit of a relation. It ties to origami. So let me start. What is origami? Most people think they know what origami is. It's this: flapping birds, toys, cootie catchers, that sort of thing. And that is what origami used to be. But it's become something else. It's become an art form, a form of sculpture.
Moj je govor "Lepršave ptice i Svemirski teleskopi." Iako bi mislili da to ne nema nikakve veze jedno s drugim, ali nadam se da ćete do isteka ovih 18 minuta, vidjeti ipak barem neku malenu poveznicu. Veže se na origami. Krenimo Što je origami? Većina ljudi misli da zna što je origami. To je ovo: Lepršave ptice, igračke, gatalice, ta vrsta stvari. A to je ono što je origami bio. Ali postao je nešto drugo. Postao je oblik umjetnosti, oblik skulpture.
The common theme -- what makes it origami -- is folding is how we create the form. You know, it's very old. This is a plate from 1797. It shows these women playing with these toys. If you look close, it's this shape, called a crane. Every Japanese kid learns how to fold that crane. So this art has been around for hundreds of years, and you would think something that's been around that long -- so restrictive, folding only -- everything that could be done has been done a long time ago. And that might have been the case.
Uobičajena tema -- ono što ga čini origamijem -- je savijanje kao način stvaranja oblika. Vrlo je star. Ovo je panel iz 1797. Pokazuje ove žene kako se igraju s igračkama. Ako pobliže osmotrite, to je ovaj oblik, zvan ždral. Svaki japanski klinac uči kako saviti ždrala. Ova je vještina bila prisutna stotine godina, pa bi pomislili da nešto što je toliko dugo prisutno -- tako ograničavajuće, samo savijanje -- sve što je moglo biti učinjeno je učinjeno prije puno vremena. I to je možda i bio slučaj.
But in the twentieth century, a Japanese folder named Yoshizawa came along, and he created tens of thousands of new designs. But even more importantly, he created a language, a way we could communicate, a code of dots, dashes and arrows. Harkening back to Susan Blackmore's talk, we now have a means of transmitting information with heredity and selection, and we know where that leads. And where it has led in origami is to things like this. This is an origami figure -- one sheet, no cuts, folding only, hundreds of folds. This, too, is origami, and this shows where we've gone in the modern world. Naturalism. Detail. You can get horns, antlers -- even, if you look close, cloven hooves.
Ali u dvadesetom stoljeću, japanski savijač imenom Yoshizawa je našao i stvorio desetke tisuća novih dizajnova. Ali čak još i važnije, stvorio je jezik, način na koji možemo komunicirati, kod točkica, crtica i strelica. Oslanjajući se na govor Susan Blackmore, sad imamo način odašiljanja informacije sa naslijeđivanjem i izabiranjem, a znamo gdje to vodi. A gdje je odvelo u origamiju su stvari poput ovih. Ovo je origami figura -- jedna ploha, bez rezova, samo savijanje, stotine preklopa To je, isto, origami, a ovo pokazuje gdje smo otišli u modernom svijetu. Naturalizam. Pojedinosti. Možete dobti rogove, roščiće -- čak, ako gledate pomno, razdijeljena kopita
And it raises a question: what changed? And what changed is something you might not have expected in an art, which is math. That is, people applied mathematical principles to the art, to discover the underlying laws. And that leads to a very powerful tool. The secret to productivity in so many fields -- and in origami -- is letting dead people do your work for you.
To potiče pitanje: što se promijenilo? A to što se promijenilo je nešto što možda ne bi očekivali u umjetosti, a to je matematika. To jest, ljudi su primijenili matematičke principe na umjetnost, da otkriju ishodišne zakone. A to vodi do jako moćnog alata. Tajna proizvodnosti u tako puno polja -- i u origamiju -- je prepuštanje mrtvim ljudima da za vas odrade vaš posao.
(Laughter)
(Smijeh)
Because what you can do is take your problem, and turn it into a problem that someone else has solved, and use their solutions. And I want to tell you how we did that in origami. Origami revolves around crease patterns. The crease pattern shown here is the underlying blueprint for an origami figure. And you can't just draw them arbitrarily. They have to obey four simple laws. And they're very simple, easy to understand. The first law is two-colorability. You can color any crease pattern with just two colors without ever having the same color meeting. The directions of the folds at any vertex -- the number of mountain folds, the number of valley folds -- always differs by two. Two more or two less. Nothing else. If you look at the angles around the fold, you find that if you number the angles in a circle, all the even-numbered angles add up to a straight line, all the odd-numbered angles add up to a straight line. And if you look at how the layers stack, you'll find that no matter how you stack folds and sheets, a sheet can never penetrate a fold. So that's four simple laws. That's all you need in origami. All of origami comes from that.
Jer ono što možete napraviti je uzeti vlastiti problem, i pretvoriti ga u problem koji je netko drugi već riješio, te iskoristiti njihova rješenje. A ja vam želim reći kako smo to učinili u origamiju. Origami se vrti oko uzoraka savijanja. Uzorak savijanja prikazan ovdje je ishodišni nacrt za origami figuru. I ne možete ih samo crtati proizvoljno. Moraju ispunjavati četiri jednostavna zakona. A ono su vrlo jednostavni, lagani za razumjeti. Prvi je zakon dvobojnost. Možete pobojati bilo koji uzorak savijanja sa samo dvije boje bez da se ikada ista boja dodiruje. Smjer preklopa na bilo kojem vrhu -- broj izbočenih nabora, broj udubljenih nabora -- uvijek se razlikuje za dva. Dva više ili dva manje. Ništa drugo. Ako gledate kuteve oko preklopa, nalazite da ako numerirate kuteve u krug, svi parni kutevi zbrojeni daju ravnu liniju, svi neparni kutevi zbrojeni daju ravnu liniju. A ako gledate kako se slojevi slažu, otkrit ćete da bez obzira kako slažete preklope i listove, list nikad ne može prodrijeti u preklop. To su četiri jednostavna zakona. To je sve što trebate u origamiju. Sav origami dolazi iz toga.
And you'd think, "Can four simple laws give rise to that kind of complexity?" But indeed, the laws of quantum mechanics can be written down on a napkin, and yet they govern all of chemistry, all of life, all of history. If we obey these laws, we can do amazing things. So in origami, to obey these laws, we can take simple patterns -- like this repeating pattern of folds, called textures -- and by itself it's nothing. But if we follow the laws of origami, we can put these patterns into another fold that itself might be something very, very simple, but when we put it together, we get something a little different. This fish, 400 scales -- again, it is one uncut square, only folding. And if you don't want to fold 400 scales, you can back off and just do a few things, and add plates to the back of a turtle, or toes. Or you can ramp up and go up to 50 stars on a flag, with 13 stripes. And if you want to go really crazy, 1,000 scales on a rattlesnake. And this guy's on display downstairs, so take a look if you get a chance.
I pomislili bi: "Mogu li četiri jednostavna zakona dopustiti nastanak ovolike složenosti?" Ali zbilja, zakoni kvantne mehanike mogu biti zapisani na ubrus, pa ipak upravljaju svom kemijom, svim životom, svom poviješću. Ako se držimo tih zakona, Možemo činiti zapanjujuće stvari. U origamiju, da bismo se držali tih zakona, možemo uzeti jednostavne uzorke -- poput ovih ponavljajućih uzoraka savijanja, zvanih teksture -- sam po sebi nije ništa. Ali ako slijedimo zakone origamija, možemo staviti ove uzorke u druge koji po sebi mogu biti nešto jako jako jednostavno, ali kad ih stavimo zajedno, dobijemo nešto malo različito. ova riba, 400 krljušti -- ponavljam, to je jedan nerazrezani kvadrat, samo savijanje. A ako ne želite savijati 400 krljušti, možete odstupiti i samo učiniti nekoliko stvari, te dodati ploče na leđa kornjače, ili prste. Ili možete pojačati i otići do 50 zvijezda na zastavi, sa 13 pruga A ako želite posve poludjeti, 1000 ljusaka na čegrtuši. A ovaj je momak izložen tu vani nešto niže, pa bacite oko ako ulovite priliku.
The most powerful tools in origami have related to how we get parts of creatures. And I can put it in this simple equation. We take an idea, combine it with a square, and you get an origami figure.
Najmoćniji alati u origamiju su se bavili kako da dobijemo dijelove stvorenja. A mogu ih staviti u ovu jednostavnu jednadžbu. Uzmemo ideju, kobiniramo je sa kvadratom, i dobijete origami figuru.
(Laughter)
(Smijeh)
What matters is what we mean by those symbols. And you might say, "Can you really be that specific? I mean, a stag beetle -- it's got two points for jaws, it's got antennae. Can you be that specific in the detail?" And yeah, you really can. So how do we do that? Well, we break it down into a few smaller steps. So let me stretch out that equation. I start with my idea. I abstract it. What's the most abstract form? It's a stick figure. And from that stick figure, I somehow have to get to a folded shape that has a part for every bit of the subject, a flap for every leg. And then once I have that folded shape that we call the base, you can make the legs narrower, you can bend them, you can turn it into the finished shape.
Ono što je bitno je što mislimo sa tim simbolima. I možete reći: "Može li se zbilja biti toliko određen? mislim, jelenak - ima dva roga kao vilice, ima antene. Može li se biti toliko određen u detaljima?" I da, zbilja se može. Pa kako to činimo? Dakle, razbijamo izradu u par manjih koraka. Neka proširim malo tu jednadžbu. Krećem sa idejom. Apstrahiram ju. Koji je najapstraktniji oblik? Štapićasti lik. A od tog štapićastog lika, nekako moram doći do savijenog oblika koji ima dio za svaki komad teme, krilce za svaku nogu. a onda jednom kad imam savijen oblik koji zovemo baza, možete napraviti noge užima, možete ih savijati, možete ih pretvoriti u završni oblik.
Now the first step, pretty easy. Take an idea, draw a stick figure. The last step is not so hard, but that middle step -- going from the abstract description to the folded shape -- that's hard. But that's the place where the mathematical ideas can get us over the hump. And I'm going to show you all how to do that so you can go out of here and fold something. But we're going to start small. This base has a lot of flaps in it. We're going to learn how to make one flap. How would you make a single flap? Take a square. Fold it in half, fold it in half, fold it again, until it gets long and narrow, and then we'll say at the end of that, that's a flap. I could use that for a leg, an arm, anything like that.
Sad prvi korak, jako je jednostavan. uzmi ideju, nacrtaj štapićast lik. Zadnji korak nije tako težak, ali taj srednji korak -- dolazak od apstraktnog opisa do savijenog oblika -- to jest teško. Ali to je mjesto gdje nas matematičke ideje mogu prevesti preko grbe. A pokazat ću vam svima kako to napraviti tako da možete otići odavde i savinuti štogod. Ali počet ćemo sa malim. Ova baza ima puno krilaca Naučit ćemo kako napraviti jedno krilce. Kako biste napravili jedno krilce? Uzmite kvadrat. Presavinite ga na pola, ponovno, presavinite ga opet, sve dok ne postane dug i uzak, i onda ćemo na kraju toga reći: 'to je krilce'. Mogu to koristiti za nogu, ruku, bilo što nalik tome.
What paper went into that flap? Well, if I unfold it and go back to the crease pattern, you can see that the upper left corner of that shape is the paper that went into the flap. So that's the flap, and all the rest of the paper's left over. I can use it for something else. Well, there are other ways of making a flap. There are other dimensions for flaps. If I make the flaps skinnier, I can use a bit less paper. If I make the flap as skinny as possible, I get to the limit of the minimum amount of paper needed. And you can see there, it needs a quarter-circle of paper to make a flap. There's other ways of making flaps. If I put the flap on the edge, it uses a half circle of paper. And if I make the flap from the middle, it uses a full circle. So, no matter how I make a flap, it needs some part of a circular region of paper. So now we're ready to scale up. What if I want to make something that has a lot of flaps? What do I need? I need a lot of circles.
Koji je papir ušao u to krilce? Pa, ako ga odmotam i vratim se na uzorak savijanja, možete vidjeti da je gornji lijevi kut tog oblika onaj papir koji je ušao u krilce. Dakle to je krilce, a sav je preostali papir višak. Mogu ga koristiti za nešto drugo. Ima i drugih načina da se napravi krilce. Ima drugih dimenzija krilca. ako učinim krilce tanjim, mogu koristiti nešto manje papira. Ako učinim krilce onoliko tankim koliko je uopće moguće, dolazim do granice minimalne količine potrebnog papira. a možete vidjeti ovjde, potrebno je četvrt kruga papira da se napravi krilce. Postoje i drugi načini izrade krilaca. Ako stavim krilce na rub, koristiti će pola kruga papira. a ako ga napravim u sredini, koristiti će puni krug. Dakle, bez obzira kako napravim krilce, traži neki dio kružne regije papira. dakle sad smo spremni na uvećanje. Što ako želim nešto što ima puno krilaca? Što trebam? Trebam puno krugova.
And in the 1990s, origami artists discovered these principles and realized we could make arbitrarily complicated figures just by packing circles. And here's where the dead people start to help us out, because lots of people have studied the problem of packing circles. I can rely on that vast history of mathematicians and artists looking at disc packings and arrangements. And I can use those patterns now to create origami shapes. So we figured out these rules whereby you pack circles, you decorate the patterns of circles with lines according to more rules. That gives you the folds. Those folds fold into a base. You shape the base. You get a folded shape -- in this case, a cockroach. And it's so simple.
A u 90-ima, umjetnici origamija otkrili su te principe i shvatili da možemo stvarati koliko god složene figure samo slažući krugove. I to je gdje su nam mrtvi ljudi počeli pomagati, Jer puno je ljudi proučavalo problem slaganja krugova. Mogu se osloniti na veliku povijest matematičara i umjetnika koji su se bavili slaganjem diskova i razmještajem. A ja sad mogu koristiti te oblike kako bih složio oblike u origamiju. Tako smo otkrili ta pravila pomoću kojih slažete krugove, ukrašavate uzorke krugova pomoću linija u skladu sa još pravila. To vam daje presavijanja. Ta presavijanja se savijaju u baze. Vi oblikujete bazu. Dobijate savijeni oblik -- u ovom slučaju, žohara. I to je tako jednostavno.
(Laughter)
(Smijeh)
It's so simple that a computer could do it. And you say, "Well, you know, how simple is that?" But computers -- you need to be able to describe things in very basic terms, and with this, we could. So I wrote a computer program a bunch of years ago called TreeMaker, and you can download it from my website. It's free. It runs on all the major platforms -- even Windows.
To je tako jednostavno da to može i računalo. Te kažete: "Pa, znate, koliko je to jednostavno?" Ali računala -- morate biti u stanju opisati stvari u posve jednostavnim pojmovima, a s tim, možemo. Pa sam napisao računalni program prije niz godina zvan TreeMaker, a koji možete skinuti s mog sajta. Besplatan je. Vrti se na svim glavnim platformama -- čak i Windowsima.
(Laughter)
(Smijeh)
And you just draw a stick figure, and it calculates the crease pattern. It does the circle packing, calculates the crease pattern, and if you use that stick figure that I just showed -- which you can kind of tell, it's a deer, it's got antlers -- you'll get this crease pattern. And if you take this crease pattern, you fold on the dotted lines, you'll get a base that you can then shape into a deer, with exactly the crease pattern that you wanted. And if you want a different deer, not a white-tailed deer, but you want a mule deer, or an elk, you change the packing, and you can do an elk. Or you could do a moose. Or, really, any other kind of deer. These techniques revolutionized this art. We found we could do insects, spiders, which are close, things with legs, things with legs and wings, things with legs and antennae. And if folding a single praying mantis from a single uncut square wasn't interesting enough, then you could do two praying mantises from a single uncut square. She's eating him. I call it "Snack Time."
Vi samo nacrtate štapićasti lik, a on izračuna uzorak savijanja. On slaže krugove, računa uzorak savijanja, a ako koristite onaj štapićasti lik koji sam vam upravo pokazao -- za koji nekako možete reći da je jelen, jer ima rogove -- dobti ćete ovaj uzorak savijanja. A ako uzmete taj uzorak savijanja i presavijete po istočkanim linijama, dobit ćete bazu koju potom možete oblikovati u jelena, sa točno onim uzorkom savijanja koji ste željeli. A ako želite različitog jelena, ne bjelorepog jelena, nego želite drugu vrstu, ili losa, promijenite slaganje, i možete napraviti soba. ili možete napravili losa. Ili, zbilja, bilo koju drugu vrstu jelena. Ove su tehnike preokrenule ovu umjetnost. Otkrili smo da možemo raditi kukce, Pauke, koji su im bliski, stvari s nogama, stvari s nogama i krilima, stvari s nogama i antenama. A ako savijanje jedne bogomoljke iz jednog nerazrezanog kvadrata nije dovoljno zanimljivo, onda možete napraviti dvije bogomoljke iz jednog nerazrezanog kvadrata. Ona ga jede. Zovem ga "vrijeme za prezalogajiti".
And you can do more than just insects. This -- you can put details, toes and claws. A grizzly bear has claws. This tree frog has toes. Actually, lots of people in origami now put toes into their models. Toes have become an origami meme, because everyone's doing it. You can make multiple subjects. So these are a couple of instrumentalists. The guitar player from a single square, the bass player from a single square. And if you say, "Well, but the guitar, bass -- that's not so hot. Do a little more complicated instrument." Well, then you could do an organ.
A možete činiti i više od samo kukaca. Ovo -- možete stavljati detalje, prste i kandže. Grizli ima kandže. Ova gatalinka ima prste. Zapravo, puno ljudi u origamiju sad stavlja prste na svoje modele. Prsti su postali meme u origamiju, jer svi ih rade. Možete uzeti višestruke teme. Tako je ovo par instrumentalaca. Svirač gitare iz jednog kvadrata. Svirač basa iz jednog kvadrata. A ako kažete: "Dobro, ali gitara, bas -- to nije takva špica. Napravite malo složeniji instrument." U redu, onda možete složiti orgulje.
(Laughter)
(Smijeh)
And what this has allowed is the creation of origami-on-demand. So now people can say, "I want exactly this and this and this," and you can go out and fold it. And sometimes you create high art, and sometimes you pay the bills by doing some commercial work. But I want to show you some examples. Everything you'll see here, except the car, is origami.
A to je omogućilo stvaranje origamija po narudžbi. Tako da sad ljudi mogu reći: "Želim točno to i to i to," a vi možete otići i saviti im što žele. Ponekad stvarate visoku umjetnost, a ponekad plačate račune odrađujući nešto komercijalno. Ali želim vam pokazati neke primjere. Sve što ćete vidjeti ovdje, osim auta, je origami.
(Video)
(Video)
(Applause)
(Pljesak)
Just to show you, this really was folded paper. Computers made things move, but these were all real, folded objects that we made. And we can use this not just for visuals, but it turns out to be useful even in the real world. Surprisingly, origami and the structures that we've developed in origami turn out to have applications in medicine, in science, in space, in the body, consumer electronics and more.
Samo da vam pokažem, ovo je zbijla bio savijeni papir. Računala su napravila da se stvari kreću, Ali to su sve bili pravi, savijeni predmeti koje smo napravili. I ne moramo ih koristiti samo za vizualne efekte, nego ispada da su korisni i u stvarnom svijetu. Iznenađujuće, origami i strukture koje smo razvili u origamiju imaju primjene u medicini, znanosti, u svemiru, tijelu, potrošačkoj elektronici i drugdje.
And I want to show you some of these examples. One of the earliest was this pattern, this folded pattern, studied by Koryo Miura, a Japanese engineer. He studied a folding pattern, and realized this could fold down into an extremely compact package that had a very simple opening and closing structure. And he used it to design this solar array. It's an artist's rendition, but it flew in a Japanese telescope in 1995. Now, there is actually a little origami in the James Webb Space Telescope, but it's very simple. The telescope, going up in space, it unfolds in two places. It folds in thirds. It's a very simple pattern -- you wouldn't even call that origami. They certainly didn't need to talk to origami artists.
I želim vam pokazati neke od tih primjera. Jedan od najranijih je bio ovaj uzorak, ovaj savijeni uzorak, koji je proučavao Koryo Miura, japanski inženjer. Proučavao je ovaj uzorak presavijanja, i shvatio da bi se dalo ispresavijati u krajnje kompaktno pakiranje koje bi imalo vrlo jednostavnu strukturu otvarajna i zatvaranja. I iskoristio ju je da osmisli ovu solarnu ploču. Ovo je umjetnički prikaz, ali poletjela je na japanskom teleskopu 1995. Sad, ima zapravo nešto malo origamija i u svemirskom teleskopu James Webb, ali je vrlo jednostavan. Teleskop, odlazeći u svemir, odmotava se na dva mjesta, Zamata se u trećinama. To je vrlo jednostavan uzorak -- ne biste ga čak niti nazvali origami. Sigurno da nisu trebali pričati sa umjetnicima origamija.
But if you want to go higher and go larger than this, then you might need some origami. Engineers at Lawrence Livermore National Lab had an idea for a telescope much larger. They called it the Eyeglass. The design called for geosynchronous orbit 25,000 miles up, 100-meter diameter lens. So, imagine a lens the size of a football field. There were two groups of people who were interested in this: planetary scientists, who want to look up, and then other people, who wanted to look down. Whether you look up or look down, how do you get it up in space? You've got to get it up there in a rocket. And rockets are small. So you have to make it smaller. How do you make a large sheet of glass smaller? Well, about the only way is to fold it up somehow. So you have to do something like this. This was a small model.
Ali ako želite ići više i graditi veće od tog, onda bi vam moglo zatrebati nešto origamija. Inženjeri u nacionalnom laboratoriju Lawrence Livermore su imali ideju puno većem teleskopu. Zvali su ga Okular. Dizajn je bio predviđen za geosinkronu orbitu na 25.000 milja, s lećom promjera 100 metara. Dakle zamislite leću veličine nogometnog igrališta. Bile su dvije grupe ljudi koje su bile zainteresirane za ovo: planetarni znanstvenici, koji su htjeli gledati gore, i onda neki drugi ljudi, koji su htjeli gledati dolje. Gledali vi gore ili dolje, kako ćete to podići u svemir? Morate doći tamo sa raketom. A rakete su malene. Tako da to trebate učiniti još manjim. Kako učiniti veliku plohu stakla manjom? Pa, jedini je način da se nekako smota. Tako da morate napraviti nešto ovakvo. Ovo je bio maleni model.
Folded lens, you divide up the panels, you add flexures. But this pattern's not going to work to get something 100 meters down to a few meters. So the Livermore engineers, wanting to make use of the work of dead people, or perhaps live origamists, said, "Let's see if someone else is doing this sort of thing." So they looked into the origami community, we got in touch with them, and I started working with them. And we developed a pattern together that scales to arbitrarily large size, but that allows any flat ring or disc to fold down into a very neat, compact cylinder. And they adopted that for their first generation, which was not 100 meters -- it was a five-meter. But this is a five-meter telescope -- has about a quarter-mile focal length. And it works perfectly on its test range, and it indeed folds up into a neat little bundle.
Savijena leća, podijelite ploče, dodate krivine Ali ovaj uzorak neće dostajati da smanjite nešto od 100 metara na samo nekoliko metara. Pa su inženjeri iz Livermora, želeći iskoristiti rad mrtvih ljudi, ili možda živih origamista, rekli: "Ajde da vidimo radi li netko drugi ovu vrstu stvari." Pa su pogledali u origami zajednicu, stupili smo u kontakt, te sam počeo raditi s njima. Pa smo zajedno razvili uzorak koji se smanjuje na proizvoljnu veličinu, ali koji dopušta bilo koji plosnati prsten ili disk da se savine u vrlo uredan, kompaktni cilindar. Usvojili su to za svoju prvu generaciju, koja nije bila 100 metara -- bila je 5 metara. ali to je 5-metarski teleskop -- s fokalnom duljinom od oko četvrt milje. I radi savršeno na svojem probnom poligonu, i zaista se sklapa u zgodan mali paket.
Now, there is other origami in space. Japan Aerospace [Exploration] Agency flew a solar sail, and you can see here that the sail expands out, and you can still see the fold lines. The problem that's being solved here is something that needs to be big and sheet-like at its destination, but needs to be small for the journey. And that works whether you're going into space, or whether you're just going into a body. And this example is the latter. This is a heart stent developed by Zhong You at Oxford University. It holds open a blocked artery when it gets to its destination, but it needs to be much smaller for the trip there, through your blood vessels. And this stent folds down using an origami pattern, based on a model called the water bomb base.
Sad, postoji i drugi origami u svemiru. Japanska aeronautička i svemirska istraživačka agencija je podigla solarno jedro, i ovdje možete vidjeti kako se jedro širi, i ovdje još vidite linije preklopa. Problem koji je riješen ovdje je nešto što treba biti veliko i nalik plohi na odredištu, ali mora biti maleno tijekom puta. a to radi išli vi u svemir, ili u tijelo. A ovo je primjer potonjeg. Ovo je srčani stent koji je razvio Zhong You sa sveučilišta u Oxfordu. On drži otvorenom blokiranu arteriju jednom kad dođe na svoje odredište, ali mora biti puno manji za put do tamo. kroz vaše krvne žile. A ovaj se stent previja koristeći uzorak iz origamija, temeljen na modelu koj se zove baza vodene bombe.
Airbag designers also have the problem of getting flat sheets into a small space. And they want to do their design by simulation. So they need to figure out how, in a computer, to flatten an airbag. And the algorithms that we developed to do insects turned out to be the solution for airbags to do their simulation. And so they can do a simulation like this. Those are the origami creases forming, and now you can see the airbag inflate and find out, does it work? And that leads to a really interesting idea.
Dizajneri zračnih jastuka također imaju problem stiskanja ravnih ploha u mali prostor. Oni žele napraviti svoj dizajn simulacijom. Pa moraju shvatiti kako, na računalu, spljoštiti zračni jastuk. A algoritmi koje smo razvili da radimo kukce je ispao riješenje za zračne jastuke da izvrše njihovu simulaciju. Tako da mogu raditi simulacije poput ove. Ovo se oblikuju origami nabori, i sad možete vidjeti kako se zračni jastuk napuhuje i promisliti, radi li? A to vodi do zbilja zanimljive ideje.
You know, where did these things come from? Well, the heart stent came from that little blow-up box that you might have learned in elementary school. It's the same pattern, called the water bomb base. The airbag-flattening algorithm came from all the developments of circle packing and the mathematical theory that was really developed just to create insects -- things with legs. The thing is, that this often happens in math and science. When you get math involved, problems that you solve for aesthetic value only, or to create something beautiful, turn around and turn out to have an application in the real world. And as weird and surprising as it may sound, origami may someday even save a life. Thanks.
Znate, otkud su ove stvari došle? Pa, srčani stent dolazi iz one male kutije na napuhavanje koju ste mogli naučiti u osnovnoj školi. To je isti uzorak, zvan baza vodene bombe. Algoritam za spljoštavanje zračnog jastuka dolazi iz svog razvoja slaganja krugova i matematičke teorije koja je zbilja bila razvijena smao da stvori kukce -- stvari s nogama. Stvar je, da se ovo često dešava u matematici i znanosti. Kada uključite matematiku, problem koji ste riješili samo radi estetske vrijednosti, ili da stvorite nešto prekrasno, se vrti uokolo i ispada da ima primjenu u stvarnom svijetu. I koliko god čudno i iznenađujuće može zvučati, origami može jednog dana čak i spasiti život. Hvala.
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