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# Mathematicians Solve Problem of Folding a Pop-up Tent

A series of experiments shed light on "overcurvature"

Image: FROM “OVERCURVATURE DESCRIBES THE BUCKLING AND FOLDING OF RINGS FROM CURVED ORIGAMI TO FOLDABLE TENTS,” BY PIERRE-OLIVIER MOUTHUY ET AL., IN NATURE COMMUNICATIONS, VOL. 3, ARTICLE NO. 1290; DECEMBER 18, 2012

Camping enthusiasts and aspiring modern sculptors take heed: researchers have achieved a breakthrough in understanding and controlling overcurvature, which is found in such disparate settings as pop-up tents, DNA plasmids and curved origami. Overcurvature occurs when a ring is too curved to lie flat in a plane the way a normal circle does. For example, if you detached a segment of a Slinky and connected its ends to make a closed loop, you would have a hard time getting the whole thing to lie flat on the floor. The intrinsic curvature of the Slinky would cause the ring to buckle and assume a three-dimensional saddle shape.

In fact, the Slinky played a major role in this research project, the results of which were published in the journal Nature Communications last December. (Scientific American is part of Nature Publishing Group.) After observing overcurved rings of various sizes and materials, the researchers found a family of curves with fairly simple mathematical descriptions that they believed would model the shapes these overcurved rings take in space. They used loops made from portions of plastic Slinkys as the setting for precise measurements and found that their predicted curves were indeed what they observed in the Slinkys. “It was really surprising to us,” says Alain Jonas, a materials scientist at the Catholic University of Leuven in Belgium, who led the research. “It was this experience where you find something and it actually fits!”

The paper includes an efficient pathway for folding pop-up tents and other overcurved rings, as shown in the illustration above. To fold a ring into three loops, place your hands on opposite sides of the ring. As you lift up, bring your hands together and grab the opposite sides in one hand. Use your free hand to coax the two opposite sides down and toward each other to form a saddle shape. At both the top and the bottom, push one side over the other and collapse the loops together.

The proposal differs from the approach that people usually take. It requires more energy initially but uses less overall. “It's not very intuitive when you do it,” Jonas says, “but that's what the physics of the problem wants.” After performing the research, he borrowed a friend's tent to practice the technique he and his colleagues had developed. It was a success.

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1. 1. scrodz 03:03 PM 2/22/13

Congratulations. You've found a way to do what butchers and carpenters have been doing since the invention of the band saw.

2. 2. DaveAlsop 10:07 PM 2/22/13

Just like the butchers, the entomologists have known about this folding trick for many years. A firm named BioQuip (in California) has for many years sold a product called a Snap Net that can be folded (as shown) and placed in a back pocket.

3. 3. DaveAlsop 10:07 PM 2/22/13

Just like the butchers, the entomologists have known about this folding trick for many years. A firm named BioQuip (in California) has for many years sold a product called a Snap Net that can be folded (as shown) and placed in a back pocket.

4. 4. Michael Bode 08:13 PM 2/23/13

Yes the butchers and woodworkers have known this information for years. Reminds me of some other old information that might be worth sharing. This is attributed to Maine boat builders, who just happen to be involved with probably the highest form of woodworking.

"Knowledge earned is better than knowledge learned, if it don't come too dear."

5. 5. UncaDonald418 10:56 PM 2/23/13

To be fair, a math whiz would have never taken a high school shop class where that skill was taught!

6. 6. rkglover 08:33 PM 2/26/13

I am facinated by new discoveries and "How the Slinky Buckles" really caught my attention.
About 60 years ago a wood working craftsman taught me how to coil a bandsaw blade. I'm sure he wasn't aware that the technique had not been discovered.

7. 7. kbbpll 12:24 PM 3/2/13

I've been folding beaded clincher bicycle tires using the method the article describes, for over thirty years. I had no idea that it was a scientific breakthrough.

8. 8. Vorut 06:24 PM 3/4/13

At least one of the bandsaw companies folds their blades into five loops. Check out your local woodworkers store.

9. 9. JayHaden 02:23 PM 3/15/13

Most surveyors of a certain age learned how to "throw a chain" using this technique. Before laser distance measuring, a chain was the surveyor's metal tape, 100 feet long, marked in decimal subunits. At day's end, the chain was coiled like a rope into loops about 5 feet in circumference. Each loop would have a half twist because of the way the chainman would reach behind himself for the next five-foot length, pulling it forward and laying it in his palm on top of the previous loops. That pile of 20 or so big loops was reduced to a handful of about 75 small loops using the technique described in this article. The chain could then be carried and stored easily without kinking. Techniques for lefties and righties were different and could create a mess if the lefty technique was used for throwing the chain and the righty method for unwinding.

10. 10. mudphud 05:29 PM 3/17/13

I'm not sure how many of the comments above are serious or joking, but there is a big difference between knowing a technique works and understanding how it works. I know how to fold a tent, but I'm pretty sure that physical knowledge wont help anyone in modeling a new application for it, at say the nanoscale or as a new way to pack things for satellites,

11. 11. rickbb 08:59 AM 3/18/13

You only want to fold a canvas pop tent, never fold a nylon tent. The constant creasing on the nylon will crack the water proofing and cause it to leak.

You just stuff the nylon one in the bag, that way it never creases in the same place.

FYI.

12. 12. evelynjlamb 06:37 PM 3/18/13

You can see a video of researcher Alain Jonas demonstrating the technique using his daughter's dress here:

13. 13. Poppa beer 03:01 AM 3/19/13

I seem to remember that my wife had a sunhat with the wide brim folding in just this way about 50 years ago.

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