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

Topological Folding Puzzle

A Topological Paper Puzzle

Oh, and for the other puzzle in my earlier post, this was a draft post originally started on 9/2/2013 which I never published, that shows the video in which I got the puzzle.




This one is pretty easy.  But still, if you need the solution:

Paperfolding Puzzle

Last Sunday was the annual Oriday Festival at the Van Nuys Japanese Gardens.  As usual, I was tasked not to teach (my friends Hisako Tanji, Joy Nishijima, and Georgia Jenkins were indoors to teach) but to entertain.

I brought along a couple of paper puzzles to keep folks entertained:






The following entry was a post originally started on 9/03/2013:



I believe this comes, via Martin Gardner's Mathematical Games columns:


Solution:

OFF at Marti's- Never Forget!

 OFF (Origami for Fun) happened on the 15th anniversary of 9/11.

I taught Heinz Strobl's Surprise/Flipp Flopp out of leftover strips from cutting 8 1/2 x 11" into squares.

It was a decent turnout, although a number of parties were absent from attendance.

Another Robert Neale trick

Here's another variation of the same trick:

Paper tricks

Single Fold Party Trick

Robert Neale's Magic Trap Door

$3 Umulius Rectangulum

Tim mentions Marti Reis at the beginning of the video (and mentions her Atlanta trip- the reason she was absent from her origami meeting this month):

Paper tricks

The Paper Levitation Puzzle

1st Sunday at Marti's

It's Super Bowl Sunday, so Jared brought the appropriate origami

Ron Fujioka brought his copy of Ken Hmoob's horse book and Jared Needle folded one

David Donahue taught his beautiful illusion box.

Alex suggested I use math to figure out the proportion for the lid in this hexagonal version of Angel Blanco's box.  But it only took me 3 trial-and-error attempts to play with it, to get the model I was after.

Secret heart box by Akiko Yamanashi

Marti's puzzle table, designed by David Wade:

More photos here.

Boldly Going Where Folders Have Gone Before

Won Park Enterprise

At Marti's last Sunday, Ron Fujioka brought a stack of bank bill $ that he had been holding onto for Fred Upton for 2 years.  Why?  Because Fred had put out a request for anyone with bills that held the numbers "1701" in its serial- the same as the serial number on the various Enterprises.

So Fred taught Won Park's version of the Enterprise last Sunday.  Fred figured it out from Won's descriptions and from some help Won gave him back when he made a visit out to Los Angeles.

Photos here.

Marti's 1st Sunday for Four May

1st two attempts at Alexandr Pak's Kawasaki rose-in-a-pot

David and his Pteranodon

I had the honor of driving the two rock stars, Yami and Joe, to the meeting on Sunday.

Hisako's been on a picture frame kick so I linked her to a video tutorial I had done years ago, showing a one-piece version of V'ann Cornelius' picture frame.  She asked for some help and I had to refresh myself on how to do it.  There's nothing quite like yourself teaching yourself.


Photos here (Arranged old to new, so scroll down).

Ron holds up a green ribbon prize

Ron Fujioka made an appearance.  Marti showed him some of her puzzles:

Marti's 1st Sunday Yesterday

Easter models seemed to be the theme.

A Pajarita Puzzle Cube

Dr. Robert Lang, via the O-List:

A couple of years ago I wrote a paper for the Journal of Mathematics and the
Arts, titled "A Pajarita Puzzle Cube in Papiroflexia", about the underlying
mathematics of a modular cube that has the silhouette of a Pajarita on each
face. The "puzzle" aspect is that even after you've folded the 12 units, it
is not at all obvious how to assemble them in such a way that one obtains a
perfect Pajarita on each face.

I just learned that for a brief time, JMA is offering the paper as a free
download (normally it's behind a paywall), and so if you'd like to fold the
units (folding instructions included), try the puzzle, or create your own
version, here's the link:

http://www.tandfonline.com/doi/full/10.1080/17513472.2013.765311

Enjoy!

Robert

P.S. Oh, and I also just learned that it was awarded "Best paper of 2014" by
the journal. That's the "tootiness" of this post.

Origami Zoetrope?

I can just picture that bird being replaced with an illustration of a flapping crane; or the Japanese woodblock carving of the magician throwing a paper into the air and having it come to life.

Zoetrope.org website:

Zoetrope is an an animated vintage toy that was originally developed in 1830s. The Zoetrope has recently been a major feature in the film, “The Woman In Black” starring Daniel Radcliffe.

This is a modern replica of a traditional Zoetrope. A zoetrope is a device that produces the illusion of motion from a rapid succession of static pictures.

The zoetrope consists of a cylinder with slits cut vertically in the sides. On the inner surface of the cylinder is a band with images from a set of sequenced pictures. As the cylinder spins, the user looks through the slits at the pictures across. The scanning of the slits keeps the pictures from simply blurring together, and the user sees a rapid succession of images, producing the illusion of motion.

Just insert an animation strip, spin the drum and look through the slots. The pictures instantly spring to life! Eagles flap, Orcas dive, frogs jump and more! Change the 18 included picture strips at will. Then, try sketching on the six included Draw-Your-Own strips. Anyone can be an animator! Our Zoetrope’s compact elegance and smooth performance remains unmatched in the world of animation toys. Originally designed by Fred DaMert and Bill Hanlon in 1992 and sold by the DaMert Company, this timeless favorite has been off the market for years. Now, with Fred’s blessing, we’ve proudly brought it back. Not only did we use the original tooling to make this durable plastic toy, we’ve faithfully reproduced and included the original twelve picture strips designed by celebrated animator Ruth Hayes. And that’s not all. We’ve added six NEW picture strips and six “Draw-Your-Own strips!” The included instruction booklet provides a history of this classic invention, explains how it works, and tells you how to bring your own drawings to life.

It doesn't appear to be on the market any longer.  If you're a decent illustrator and like craft projects, perhaps you could make your own?  Maybe I'll do one, myself.


Ok....I just ran "zoetrope origami" through the YouTube search engine, not expecting to find anything, but- wow!  This is more impressive-looking than the one I had pictured in my mind:

 Here's another method for making one.  Upon further surfing through the web, it appears that Merry Claude actually folded a zoetrope!

Interesting idea; but I can't really make out the images all that well from this video clip.



More from Wikipedia:

Origami Furnishings

The Unfolding Apartment:

Eric Scneider's amazing space saving unfolding apartment fits neatly into one wall - a wall that interior designer Michael Che was able to fit a kitchen, closet, bed, bathroom and office into.

How about some unfolding furniture?  Or Japanese  puzzle furniture?

Stop Playing with Yourself:

History of the 5 Pigs Puzzle

The first time I saw this (and another related one) was at my first OUSA convention.  It might have been Cyril Tessier who had them to give out.  I still have them somewhere.


Puzzle of the Five Pigs

History behind it, according to psywarrior.com:

For many years prior to WWII various venders made and sold puzzles to children.  These puzzles had a number of different pictures on the front, and when folded in a special complex way depicted a hidden picture of an old man, or sometimes a political laeder, sports figure or movie star.

Pig Puzzle

During WWII the British Special Operations executive is believed to have produced a number of different puzzles showing four pigs on the front, that when folded depicted the face of Adolf Hitler.  At least four types of the pig puzzle are known, and it is believed that besides being used in Allied countries as a morale booster, they were also shipped to partisans in Nazi-occupied nations to attack and belittle the German Fuhrer.

One type with English text says, "Fold as directed to find the biggest pig of all."  Another English-language puzzle says, "Puzzle of the pig.  Here is the puzzle of the fifth pig.  To find a fifth one fold as directed."  A third puzzle is found in both French and English and was also distributed in Australia.  

~~~

Apparently, many of these puzzles were also dropped by the Royal Air Force.  In 2008, I received a letter that stated:

My father came to Canada from the Netherlands in the 1950s.  When he was a young man in Holland during the war he collected different things.  He has a paper he said they threw out of an airplane.  It is written in Dutch and English.  "Can you find the 5th pig." There are four pigs on the picture, and when folded right the four pigs together make a face that resembles Hitler.

Some more people mentioning inheriting one of these from a grandparent.

If anyone has anymore information on the background and history of this and related, let me know.