Mathematician Shows How to Make Any Shape From a Single Cut

Mathematicians don’t approach the world quite like the rest of us. Case in point: Katie Steckles. The Manchester-based mathematician was trying to cut a square out of a piece of paper and started to wonder about the most efficient way to do so. Her queries led her to some experimentation (turns out it can be done with one snip), and then to the pub, where she wondered aloud whether there were other shapes that could be made with one cut. Her companion asked, “Isn’t that a theorem?”

Indeed it is. The fold-and-cut theorem, which first appeared in 1721—and was later proved by MIT computer scientist/computational origami wizard/former child prodigy Erik Demaine—asserts that any shape comprised of straight lines can be made from a single cut if you can just figure out the right way to fold the paper. Stars, turtles, the entire alphabet—which Steckles demonstrates in the Numberphile video above—can all be crafted. The concept is pretty mind-blowing and, as you’ll learn from Steckles, might’ve even earned Betsy Ross her place in history. 

[h/t The Kids Should See This]

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Afternoon Map
The Most Popular Infomercial Product in Each State

You don't have to pay $19.95 plus shipping and handling to discover the most popular infomercial product in each state: AT&T retailer All Home Connections is giving that information away for free via a handy map.

The map was compiled by cross-referencing the top-grossing infomercial products of all time with Google Trends search interest from the past calendar year. So, which crazy products do people order most from their TVs?

Folks in Arizona know that it's too hot there to wear layers; that's why they invest in the Cami Secret—a clip-on, mock top that gives them the look of a camisole without all the added fabric. No-nonsense New Yorkers are protecting themselves from identity theft with the RFID-blocking Aluma wallet. Delaware's priorities are all sorted out, because tons of its residents are still riding the Snuggie wave. Meanwhile, Vermont has figured out that Pajama Jeans are the way to go—because who needs real pants?

Unsurprisingly, the most popular product in many states has to do with fitness and weight loss, because when you're watching TV late enough to start seeing infomercials, you're probably also thinking to yourself: "I need to get my life together. I should get in shape." Seven states—Colorado, Idaho, Kentucky, Montana, Nebraska, Utah, and Wisconsin—have invested in the P90X home fitness system, while West Virginia and Arkansas prefer the gentler workout provided by the Shake Weight. The ThighMaster is still a thing in Illinois and Washington, while Total Gym and Bowflex were favored by South Dakota and Wyoming, respectively. 

Kitchen items are clearly another category ripe for impulse-buying: Alabama and North Dakota are all over the George Forman Grill; Alaska and Rhode Island are mixing things up with the Magic Bullet; and Floridians must be using their Slice-o-matics to chop up limes for their poolside margaritas.

Cleaning products like OxiClean (D.C. and Hawaii), Sani Sticks (North Carolina), and the infamous ShamWow (which claims the loyalty of Mainers) are also popular, but it's Proactiv that turned out to be the big winner. The beloved skin care system claimed the top spot in eight states—California, Mississippi, Nevada, New Mexico, Oklahoma, Oregon, Tennessee, and Texas—making it the most popular item on the map.

Peep the full map above, or check out the full study from All Home Connections here.

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Design
A Florida Brewery Created Edible Six-Pack Rings to Protect Marine Animals

For tiny scraps of plastic, six-pack rings can pose a huge threat to marine life. Small enough and ubiquitous enough that they’re easy to discard and forget about, the little plastic webs all too often make their way to the ocean, where animals can ingest or become trapped in them. In order to combat that problem, Florida-based Saltwater Brewery has created what they say is the world’s first fully biodegradable, compostable, edible six-pack rings.

The edible rings are made of barley and wheat and are, if not necessarily tasty, at least safe for animals and humans to ingest. Saltwater Brewery started packaging their beers with the edible six-pack rings in 2016. They charge slightly more for their brews to offset the cost of the rings' production. They hope that customers will be willing to pay a bit more for the environmentally friendly beers and are encouraging other companies to adopt the edible six-pack rings in order to lower manufacturing prices and save more animals.

As Saltwater Brewery president Chris Gove says in the video above: “We want to influence the big guys and kind of inspire them to also get on board.”

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