What Origami Sorcery is This?!

From 2-dimensions into the realm of the ambient third dimension, a large circular coaster can pass through a small square hole...

Can you pass a circular disk through a slightly smaller square hole? 

Instinct tells you no. But you haven’t seen this latest video from Numberphile, in which Standford University’s Tadashi Tokieda demonstrates that, by folding a sheet of paper in just the right way, a round peg really can go in a square hole. 

“I made a square hole in this sheet of paper, and a coaster, a circular coaster,” explains Tokieda in the video. “I fold the paper in a mysterious fashion, and I can pass the coaster through the hole.” 

But, as Tokieda stresses, he is not cheating at all. “I didn’t stretch, let alone tear, and yet when I fold the sheet back in a judicious way, the coaster does go through the square that is bigger than the hole. How is this possible?” 

Well thankfully for the likes of you and me, Tokieda doesn’t leave us baffled for too long, and gets down to explaining exactly how he achieved the seemingly impossible. 

“I’m willing to give away the secret for free on this occasion,” Tokieda says. “It has to do with the intrinsic, or inner dimension, of this piece of paper, which is two dimensions, and the fact that this sheet evolves, or flourishes, in the ambient three dimensional space. There is some elbow room, there is some ambient space.” 

Ahhh, well I’m glad that’s cleared up! 

Nope? Still as confused as us? Well it has to do with the fact that, while in two dimensions the hole is indeed too small for the coaster to fit through, by taking the paper into three dimensions, you are able to bring two sides of the square together, which forms a wider slit than the disk and allows it to pass through. 

“This is all possible because when we do this maneuver, you’re allowing the whole thing to come out into 3D and then come back down [into 2D],” Tokieda continues. “This fact that you can escape into the ambient third dimension and come back in... gives you this.”

Hat tip:  British Origami Society

Engineering with Origami

Hat tip:  Andrew Hans

Breaking Standard Laws of Origami

National Geographic:

A group of researchers led by Andres Arrieta, assistant professor of mechanical engineering at Purdue University, recently published a paper in Science about how earwigs’ wings work. When the team tried to model the unfolding mechanism using a traditional understanding of origami-like folding, it did not compute. The wings simply do not fold like typical well-known materials (think paper) at a single crease.
Instead, Arrieta’s team found that the wings work by possessing spring-like folds, which have two stable configurations. He likens them to slap bracelets, which can stably switch between two different orientations.
Julia Deiters, a researcher at Germany’s University of Duisburg-Essen who recently co-authored a study on the topic, says the wings are also stabilized by folds that are bended, as opposed to straight. These arrange mechanical forces in a way that enables the wings to “lock,” either when they are completely open or folded up.

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Arrieta and others hope to use their insights into the wings’ mechanisms to create mimics in the future. “The wing gave us the recipe to make similar manmade materials,” he says. Such materials could be an invaluable tool with potential applications for making things like quick-assembly tents, portable solar panels, and compact electronics.

"Folding a New Tomorrow: Origami Meets Math and Science," Thomas Hull

How Origami is Inspiring Scientific Creativity

Houston, We Have Paper....

10 years ago...






 Try folding one yourself.

Artificial Muscle

LATimes

Scientists at the Massachusetts Institute of Technology and Harvard University have developed a variety of origami-inspired artificial muscles that can lift up to a thousand times their own weight — and yet be dexterous enough to grip and raise a delicate flower. 

The devices, described in the Proceedings of the National Academy of Sciences, offer a new way to give soft robots super-strength, which could be used everywhere from inside our bodies to outer space.

Hat tip:  Joseph Wu Inc.

Great Big Story

Toot from Dr. Lang, via Origami-L:

I don’t know if it’s really a great BIG story, but CNN did a nice little story on my folding:


http://www.greatbigstory.com/stories/folded-universe-the-astonishing-beauty-of-origami/


A few errata:


(1) There’s a few errors in their chronology on that page. I’ve sent them corrections. Until then, FAKE NEWS! Sad!


(2) At one point, I seem to be saying I invented an airbag. Which is wrong. (I contributed to an airbag algorithm.) I expect the Senate to investigate.


(3) I borrowed a line from Marty Demaine in BTF at one point. Marty, your royalty check is in the mail.


Other than all that, I hope you like it.

CNN:

The Aegis of Origami

Portable shield inspired by origami:

The device, developed by Brigham Young University—a private research university in Utah—is a foldable kevlar shield designed to protect officers in high-risk situations. The foldable shield weighs only a little bit more than a suitcase and is made from 12 layers of bullet-proof kevlar. Its folding design was also inspired by origami.

Despite its low weight, the shield is capable of stopping a .44 Magnum, 9mm, and .355 Magnum, according to reports. We will keep you posted on whether or not departments start implementing this device. 

Going from medieval to state of the art through the ancient art of origami technology:

When mechanical engineering professor Larry Howell began work on a new ballistic shield, police officers told him that their current gear was “kind of medieval.”

“Most of them are still basically just … a big chunk of steel with handles on it, and so they tend to be very heavy,” he tells The Christian Science Monitor in a phone interview. Many of them weigh nearly 100 pounds.

But a new folding kevlar shield, developed by Professor Howell, his colleague Terri Bateman, and other faculty and graduate students at Brigham Young University, weighs 55 pounds, fits in the trunk of a car, unfolds in seconds, and covers more than one officer. It can also take a hit from a .44 Magnum handgun without ripping or tipping over.

Together, these features could make the shield much better-suited to police work than current technology.

“It's easily transportable, and it provides protection for more than one officer,” says Chuck Wexler, executive director of the Police Executive Research Forum, after watching video of the shield in action. “So I think that if the test results hold up, this could be an important option for police departments to consider.”

The BYU team derived these advantages from an unlikely source. “Origami artists, over the centuries, had discovered interesting ways to achieve motion that we wouldn't have discovered using our traditional engineering approaches,” Howell explains.

His past work has used origami techniques to shrink NASA payloads and medical devices. Through discussions with federal agents and local police, “We realized that having a compact bulletproof barrier that's easy to transport, easy to stow, and then deploys very quickly, and is light, has a lot of benefits.”

“It seems kind of weird that you could go from origami … to something that's bulletproof,” Howell acknowledges. But by applying a Yoshimura fold pattern to a sheet with 12 layers of Kevlar – plus an aluminum core for stability – the researchers created a shield that can withstand hits from 9-millimeter, .357 Magnum, and .44 Magnum pistols.

A federal agent involved in the testing “said that it was revolutionary,” Howell remembers.

Origami Revolution on PBS

Haven't even sat down for time to watch this, yet; but the whole community has been buzzing about it.






According to Seth Friedman through "Google trends", searches are up 46% on origami since the NOVA airing.

The Science of Origami with Bernie Peyton

Exponential Explosion of Origami Evolution, Revolution, and Innovation

Lecture 5: Artistic Origami Design

How to Trisect an Angle with Origami

Hat tip:  Jo Nakashima


*UPDATE 12-14-2014*

Saadya on the O-List makes a great point:

The video is lovely, but I can't help being annoyed that the first discoverer of a method to use origami to solve this problem--Hisashe Abe of Hokkaido University--is nowhere  in the video (body or credits) mentioned by name. It is as if origami is this general pool of knowledge and there are no pioneers worth crediting for their efforts or discoveries. (Meanwhile in this presenter's companion video on "Euclid's Big Problem", Galois and Wantzel--mathematicians--ARE mentioned by name.)

Simple method of dividing paper into equal parts

I first learned this method from Yami Yamauchi at WCOG:

Thomas Hull on Computer-Generated Origami

Is it cheating or somehow less humanly artistic to create origami through computer programs?

Boing Boing (video is 2 years old):

Part one is here.

Via Sok Song > Vanessa Gould > Thomas Hull.

Origami in Space

Via Dr. Robert Lang to the O-List:

In the 21^st century, origami has caught the attention of engineers who are using it to create all sorts of new structures--from collapsible packaging to airbags for cars. Origami has even found its way into space!
With support from the National Science Foundation (NSF), mechanical engineer Larry Howell and a team of researchers from Brigham Young University collaborated with NASA to design a solar array that can be tightly compacted for launch and then deployed in space to generate power for space stations or satellites.

The collaboration began when Howell received an NSF grant to explore combining origami with his focus on compliant mechanisms, which are typically single-piece structures that are jointless and flexible.

Read the article at the National Science Foundation.

Origami Solar Array Prototype

After two years of research, the space agency has come closer to that goal by creating a solar array with a diameter of 8.9ft (2.7 metres) when folded and 82ft (25 metres) when unfurled.

The design, which looks like a flower blooming, was created by Nasa mechanical engineer, Brian Trease.

 

 

Mr Trease partnered with researchers at Brigham Young University in Provo, Utah, to pursue the idea that spacecraft could be built using origami folds.

Sending the solar arrays up to space would be easy, Mr Trease said, because they could all be folded and packed into a single rocket launch, with 'no astronaut assembly required.'

 

Panels used in space missions already incorporate simple folds, collapsing like a fan or an accordion.

One technique that has been used for an origami-inspired solar array is called a Miura fold invented by Japanese astrophysicist Koryo Miura.

When you open the structure, it appears to be divided evenly into a checkerboard of parallelograms.

With this particular fold, there's only one way to open or close it: Pull on one corner and the whole thing is open with only a tiny amount of effort.

Mr Miura intended this fold for solar arrays, and in 1995 a solar panel with this design was unfolded on the Space Flyer Unit, a Japanese satellite.

 

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The fold that Mr Trease and colleagues used is not a Miura fold, but rather a combination of different folds.

Mr Trease's prototype looks like a blooming flower that expands into a large flat circular surface.

Mr Trease envisions that foldable solar arrays could be used in conjunction with small satellites called CubeSats.

And he says the origami concept could be used in antennas as well. It could be especially appropriate for spacecraft applications where it's beneficial to deploy an object from the centre, outward in all directions.

Origami was originally intended for folding paper, which has almost no thickness, so Mr Trease and colleagues had to be creative when working with the bulkier materials needed for solar panels.

'You have to rethink a lot of that design in order to accommodate the thickness that starts to accumulate with each bend,' he said.

The art has been the subject of serious mathematical analysis only within the last 40 years, Mr Trease said.

There is growing interest in integrating the concepts of origami with modern technologies.

'You think of it as ancient art, but people are still inventing new things, enabled by mathematical tools,' he said.

 

 

 Previous post:

Origami in Space: BYU-designed solar arrays inspired by origami

 

 

 

 

 

the geometry of paper folding in electronics

Professor Stavros Georgakopoulos holds an origami-infused foldable antenna prototype. Florida International University

When talking about the intersection of art and science, Stavros Georgakopoulos likes to quote Albert Einstein, who once said, "I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge."

"It's absolutely true. If we became engineers and we stuck always to the book, there wouldn't be new breakthroughs," said Georgakopoulos, an electromagnetics specialist and assistant professor in Florida International University's department of electrical and computer engineering.

"Where does imagination come from? Art. Artists don't have any laws, or limits," he added.
It's from this line of thinking that Georgakopoulos is helping transform the field of electrical engineering and electronics design using the mathematical properties of a paper crane. 

The art of origami, he says, is the key to unlocking whole new conceptual modes of thought for scientists.

While folding smartphones into your jacket pocket like the front page of a newspaper is still a futurist fantasy, electronics that compress and change shape are now possible if designed the right way. They're currently in development, aided by Japan's centuries-old paper-folding techniques, an art form that spread worldwide around the mid-1900s.

Read the rest.

Hat tip:  Chila Caldera

UBC researcher creates self-folding paper product

Hat tip to Joseph Wu:

Ata Sina, a master’s student in mechanical engineering, combines the art of making Japanese origami with science to make multi-dimensional figures using paper and heat — which he later hopes to turn into commercial ventures.

To make the items, he takes sheets of paper and uses a computer program to make small cuts and creases in them. He then attaches special thermoplastic polymers onto the paper and sticks it in an oven at 110 degrees C for 10 to 20 seconds.

“When the heat hits the polymers they start shrinking and the paper starts folding into a 3D structure we have designed,” he said.

“We use software to simulate the folding. Then we kind of calculate the angles we need.”
Within seconds, the paper transforms into 3D objects. It could change into a fun toy for your kid, ornaments for your Christmas tree or something that can be used to help package fragile objects in a box to replace those Styrofoam noodles.

Although Sina will begin by making a children’s book, with fun pages kids can tear out and heat up to make shapes, he hopes to one day make packaging for commercial use and insulation for construction companies.

The Vancouver Sun asked Sina to identify five practical future uses for his product.

Here’s what he came up with:

Read the rest