Sunday, November 24, 2019

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

Article in the NYTimes

The Modern Life of Origami, an Art as Old as Paper

Precision is key, whether folding a humble crane or an interlocking modular structure. So is enthusiasm.

Written by Kathleen Massara

Photographs by Ryan Jenq

“I would say the biggest rule is no cutting,” said Wendy Zeichner, the president and chief executive of OrigamiUSA. It’s “one piece of paper and no glue.”
OrigamiUSA is a nonprofit organization dedicated to educating the public about the art form. The group traces its roots to the 1950s, when Lillian Oppenheimer, one of its eventual founders, began to communicate with paper folders around the world, including Akira Yoshizawa in Japan, who is often credited as the father of modern origami — they would send each other diagrams explaining how to fold different shapes from a single square sheet of paper. Decades later, OrigamiUSA has around 1700 paying members, and it keeps track of nearly 90 community origami groups in the United States.
Origami as an art reaches back thousands of years. “Origami is really almost as old as paper,” Ms. Zeichner explained — it means “to fold paper” in Japanese — and paper in sheet form is thought to have been invented in China around 105 A.D. To start making shapes like cranes and frogs, it boils down to two basic techniques: mountain folds and valley folds, which are different ways to make the edges meet. After that, you can get creative