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5 Math-Based Home Hacks That Will Make Your Life Easier

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Even those who like math may struggle to see how it applies to their everyday lives; even those who grant that mathematics underpins marvels from cybersecurity to moon landings may doubt the discipline’s relevance to matters mundane or domestic. Many problems routinely encountered around the house, however, do in fact benefit from mathematical methods and insights. Here’s a selection.

1. FOLDING A FITTED SHEET

To those who lack mathematically-inclined minds, mathematicians have out-of-this-world intelligence—and, with it, the ability to perform impossible feats. Folding a fitted sheet, for example.

“You should be able to figure out how to fold a fitted sheet,” an acquaintance once told Mathematical Association of America ambassador James Tanton. “It’s just topology, after all.” (Topology is the mathematical study of properties that are preserved under such deformations as stretching, crumpling, and bending, but with no tearing or gluing allowed.)

Thus goaded, Tanton brought his mathematical training to bear on the problem. Applying such tried-and-true strategies as working backwards and following your nose, he produced an instructional video (above) that will have you tidily storing elasticized bedclothes in no time. First, hold up the sheet so that the short sides are perpendicular to the floor, then stick your hands into the top two corners. Next, bring your hands together; hold the corners with one hand still inside the sheet and pull the outer corner over that hand. Lay the sheet on the table and attend to the messy side, tucking the inner corner inside the outer corner. Pick up the sheet by the corners and shake it, then lay it on the table again; once you've fixed any lingering messiness, the elastic should form an upside-down U-shape, and the sheet itself should be a rectangle. Looking at the upside-down U, fold the right side over to the left side, turn 90 degrees and fold in thirds. Finally, turn it 90 degrees and fold in thirds again, and voilà! A fitted sheet folded just as neatly as a flat sheet.

2. FLIPPING A MATTRESS

Unless it boasts a must-face-up pillow-top, a mattress can be placed on a bed frame four different ways. There are two possible sleep surfaces, each of which has two possible orientations (since one or the other short side must be at the head of the bed). For minimal wear, a mattress should spend equal time in each of the four configurations. But how is an absent-minded mattress owner to accomplish this? Is there a certain mattress maneuver that could be performed quarterly to cycle through the four arrangements?

Science writer Brian Hayes explored this question in his 2005 American Scientist article “Group Theory in the Bedroom.” Group theory is a branch of mathematics that’s handy for studying symmetry, and Hayes’s article offers an accessible introduction. Hayes ends up establishing, however, that there is no “golden rule of mattress flipping,” no maneuver one can mindlessly execute to hit each arrangement in turn.

But we're not doomed to a future of unevenly worn sleep surfaces. Hayes suggests that scrupulous sleepers do the following: Number the four mattress orientations 0, 1, 2, and 3, labeling each with a number in the corner closest to the righthand side of the head of the bed. Then, cycle through the orientations 0, 1, 2, 3, 0, 1, 2, 3, 0, etc., each quarter turning the mattress to position the next number in the upper right. Problem solved.

3. DIVIDING RENT

Suppose a handful of housemates must decide who will pay how much rent. They could just divide the total evenly, or perhaps base the division on the relative square footage of the various bedrooms. Experts in a field called "fair division," though, have a better way, one that can account for differing views on what’s valuable in a room—one roommate might crave natural light, while another would readily trade sunshine for a walk-in closet or a straight shot to the loo. The math-based method, which works thanks to a 1928 result called Sperner's Lemma, is also envy-free, meaning that no one will want to swap his room/rent payment pair for someone else's.

Mathematician Francis Su applied Sperner’s Lemma to rent partitioning in a 1999 paper [PDF]; The New York Times sketched the procedure in a 2014 article; and earlier this year “Mathologer” Burkard Polster explicated the Times piece in a 15-minute video. Online tools such as this one, however, allow would-be housemates to generate everybody’s-happy rent divisions just by entering number of housemates and total rent and then each answering a series of questions of the form “If the rooms have the following prices, which room would you choose?” As you go through the calculator, it narrows down the price range each roommate finds acceptable for each room and then finds a region where all the roommates have a room at a price they consider fair.

Users must, of course, keep their expectations realistic. If two people want the same room and are willing to pay anything for it—even if that means the other rooms are free—then the calculator won’t work. But there are also sociological concerns. “It is unfortunately beyond the scope of any algorithm,” cautions the rent calculator’s disclaimer, “to keep you from envying your roommate’s job, sex life or wardrobe—or save you from buyer’s remorse.”

4. CUTTING A CAKE

Portion envy can poison a party. So a host doling out any continuous foodstuff—cake, pizza, a 6-foot submarine sandwich—would do well to heed insights gleaned from the study of fair division.

If two people are sharing a dessert or an entree, of course, the problem is simple enough: Person A divides the dish into two portions she deems equal—maybe the piece of cake with the buttercream rose is smaller than the one without, to account for A’s taste for that decoration—and then Person B claims the portion she prefers. This division, like the rent partitioning discussed above, is envy-free: Neither person would rather have the other’s share.

Two-party division has been understood since biblical times, and a method of producing an envy-free division among three parties has been known for more than 50 years (see this article for an illustrated explanation of the cutting and trimming involved). A comparable procedure for more than three parties proved elusive until 2016, however, when computer scientists Simon Mackenzie and Haris Aziz outlined “a discrete and bounded envy-free cake cutting protocol for four agents” [PDF]. The pair subsequently adapted their protocol to cover any number of agents [PDF], but there’s a catch: Dividing a cake among even a handful of would-be eaters can require more steps than there are atoms in the universe. So hosts who want to serve their guests before staleness sets in may need to risk a little envy.

5. MOVING A SOFA

Anyone with 1) an L-shaped hallway leading from door to living room and 2) a fondness for multi-person upholstered seating may face the so-called “moving sofa problem.” Posed (more abstractly) in 1966 by mathematician Leo Moser, the problem asks for the largest sofa (in terms of seating area) that can be maneuvered around a right-angled corner without lifting, squishing, or tilting.

A square sofa with the same width—1, say—as the hallway could fit by scooting into the corner and then changing direction, but would have an area of only 1. A semicircular sofa with radius 1 would arc around nicely by using the curve to swing around the inside corner and increase the area to about 1.57. Mathematicians John Hammersley and Joseph Gerver devised corner-clearing sofa shapes, both reminiscent of old telephone handsets, with areas approximately 2.2074 and 2.2195, respectively. No one is sure that a couch made to Gerver’s specifications—the outline of the seating area comprises no fewer than 18 pieces—would be the largest one capable of rounding the corner, but it’s the best bet to date.

But what if a sofa must turn twice, once to the right and once to the left, to reach its final resting place? Mathematician Dan Romik puzzled over this variation on the moving sofa problem in recent years, and discovered a two-lobed “ambidextrous sofa” shape with area about 1.64495. The Romik Ambiturner may be the largest possible, but nothing has been proven yet. Interested readers can browse (animated!) sofa shapes on Romik's website.

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Pop Culture
5 Bizarre Comic-Con News Stories from Years Past
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At its best, Comic-Con is a friendly place where like-minded people can celebrate their pop culture obsessions, and each other. And no one can make fun of you, no matter how lazy your cosplaying might be. You might think that at its worst, it’s just a series of long lines of costumed fans and small stores crammed into a convention center. But sometimes, throwing together 100,000-plus people from around the world in what feels like a carnival-type atmosphere where anything goes can have less than stellar results. Here are some highlights from past Comic-Con-tastrophes.

1. MAN IN HARRY POTTER T-SHIRT STABS ANOTHER MAN IN THE FACE—WITH A PEN

In 2010, two men waiting for a Comic-Con screening of the Seth Rogen alien comedy Paul got into a very adult argument about whether one of them was sitting too close to the other. Unable to come to a satisfactory conclusion with words, one man stabbed the other in the face with a pen. According to CNN, the attacker was led away wearing handcuffs and a Harry Potter T-shirt. In the aftermath, some Comic-Con attendees dealt with the attack in an oddly fitting way: They cosplayed as the victim, with pens protruding from bloody eye sockets.

2. MEMORABILIA THIEVES INVADE NEW YORK

Since its founding in 2006, New York Comic Con has attracted a few sticky-fingered attendees. In 2010, a man stole several rare comics from vendor Matt Nelson, co-founder of Texas’ Worldwide Comics. Just one of those, Whiz Comics No. 1, was worth $11,000, according to the New York Post. A few years later, in 2014, someone stole a $2000 “Dunny” action figure, which artist Jon-Paul Kaiser had painted during the event for Clutter magazine. And those are just the incidents that involved police; lower-scale cases of toys and comics disappearing from booths are an increasingly frustrating epidemic, according to some. “Comic Con theft is an issue we all sort of ignore,” collector Tracy Isenhour wrote on the blog of his company, Needless Essentials, in 2015. “I am here to tell you no more. It’s time for this garbage to stop."

3. CATWOMAN SAVES THE DAY

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Adrianne Curry, winner of the first cycle of America’s Next Top Model, has made a career of chasing viral fame. Ironically, it was at Comic-Con in 2014 that Curry did something truly worthy of attention—though there wasn’t a camera in sight. Dressed as Catwoman, she was posing with fans alongside her friend Alicia Marie, who was dressed as Tigra. According to a Facebook post Marie wrote at the time, a fan tried to shove his hands into her bikini bottoms. She screamed, the man ran off, and Curry jumped to action. She “literally took off after dude WITH her Catwoman whip and chased him down, beat his a**,” Marie wrote. “Punched him across the face with the butt of her whip—he had zombie blood on his face—got on her costume.”

4. MAN POSES AS FUGITIVE-SEEKING INVESTIGATOR TO GET INTO VIP ROOM

The lines at Comic-Con are legendary, so one Utah man came up with a novel way to try and skip them altogether. In 2015, Jonathon M. Wall tried to get into Salt Lake Comic Con’s exclusive VIP enclave (normally a $10,000 ticket) by claiming he was an agent with the Air Force Office of Special Investigations, and needed to get into the VIP room “to catch a fugitive,” according to The San Diego Union Tribune. Not only does that story not even come close to making sense, it also adds up to impersonating a federal agent, a crime to which Wall pleaded guilty in April of this year and which carried a sentence of up to three years in prison and a $250,000 fine. In June, prosecutors announced that they were planning to reduce his crime from a felony to a misdemeanor.

5. MAN WALKS 645 MILES TO COMIC-CON, DRESSED AS A STORMTROOPER, TO HONOR HIS LATE WIFE

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In 2015, Kevin Doyle walked 645 miles along the California coast to honor his late wife, Eileen. Doyle had met Eileen relatively late in life, when he was in his 50s, and they bonded over their shared love of Star Wars (he even proposed to her while dressed as Darth Vader). However, she died of cancer barely a year after they were married. Adrift and lonely, Doyle decided to honor her memory and their love of Star Wars by walking to Comic-Con—from San Francisco. “I feel like I’m so much better in the healing process than if I’d stayed home,” he told The San Diego Union Tribune.

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10 Pieces of Lying Lingo from Across the United States
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Maligner. Fabricator. Fibber. Con artist. There are all sorts of ways you can say "liar," but in case you're running out, we’ve worked with the editors at the Dictionary of American Regional English (DARE) to come up with 10 more pieces of lying lingo to add to your storytelling stash.

1. HASSAYAMPA

This term for a liar originally referred to a gold-rusher in Arizona, according to DARE. It can also be used to describe an old-timer, especially one who likes to exaggerate. The word hassayampa (also hassayamper) comes from the Hassayampa River, which is located in the Grand Canyon State. According to the Dictionary of American Folklore, “There was a popular legend that anyone who drank of the Hassayampa River in Arizona would never again tell the truth.”

2. JACOB

“You’re a Jacob!” you might say to a deceiver in eastern Alabama or western Georgia. This word—meaning a liar, a lie, and to lie—might be based on the Bible story of twin brothers Jacob and Esau. Esau, the elder and firstborn, stood to inherit his parents' estate by law. At the behest of his mother, Jacob deceived their father, blinded in old age, into thinking he was Esau and persuaded him to bestow him Esau’s blessing.

3. LIZA

Liza or Liza Jane can mean a lie or a liar. Hence, to lizar means to lie. Like Jacob, Liza is an eastern Alabama and western Georgia term. However, where it comes from isn’t clear. But if we had to guess, we’d say it’s echoic of lies.

4. STORY

“What a story you are,” you might say to a prevaricator in Virginia, eastern Alabama, or western Georgia. According to the Oxford English Dictionary (OED), story, meaning a liar, is mainly used in the phrase, “You story!” Story as a verb meaning “to give a false or malicious account, lie, tattle,” is an English dialect word, according to DARE, and is chiefly used in the South and South Midland states. “You storied to me about getting a drink,” you might tell someone who stood you up.

5. LOAD

To load or load up means to trick, mislead, or “deceive by yarns or windies,” according to cowboy lingo in northwest Texas. The term, which can also be a noun meaning a lie or liar, might also be heard in northwest Arkansas and the Ozarks.

6. YARN

To spin a yarn, or to tell a long tale, began as nautical slang, according to the OED, and comes from the idea of telling stories while doing seated work such as yarn-twisting. (The word yarn comes from the Old English gearn, meaning "spun fiber, spun wool.") By extension, a yarn is a sometimes marvelous or incredible story or tale, and to yarn means to tell a story or chat. In some parts of the U.S., such as Arkansas, Indiana, Maryland, and Tennessee, to yarn means to lie or tell a falsehood. “Don’t yarn to me!” you might say. Street yarn refers to gossip in New York, Kentucky, and parts of New England.

7. WINDY

Telling a windy in the West? You’re telling an “extravagantly exaggerated or boastful story,” a tall tale, or a lie, says DARE. Wind has meant “vain imagination or conceit” since the 15th century, says OED.

8. LIE

In addition to being a falsehood or tall tale, a lie in the South and South Midland states can refer to the liar himself.

9. STRETCH THE BLANKET

You’ve probably heard of stretching the truth. How about stretching the blanket? This phrase meaning to lie or exaggerate is especially used in the South Midland states. To split the blanket, by the way, is a term in the South, South Midland, and West meaning to get divorced, while being born on the wrong side of the blanket means being born out of wedlock, at least in Indiana and Ohio.

10. WHACK

In the South and South Midland, whack refers to a lie or the act of lying. It might come from the British English colloquial term whacker, meaning anything abnormally large, especially a “thumping lie” or “whopper,” according to the OED. In case you were wondering, wack, as in “crack is wack,” is probably a back-formation from wacky meaning crazy or odd, also according to the OED. Wacky comes from whack, a blow or hit, maybe from the idea of being hit in the head too many times.

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