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.

11 Everyday Tasks That Are Tricky for Left Handers

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In Medieval times, left-handed people had more to worry about than smudging their own handwriting: Being a lefty was associated with demonic possession. While those with southpaw tendencies aren't likely to be labeled as the devil's puppet today, life for those in that 10 percent of the population can still be a struggle. In honor of International Left Handers Day, check out some common tasks that lefties rarely get right.

1. USING SCISSORS

Unless you special-order left-handed scissors, the act of cutting up paper can quickly become an exercise in frustration. Scissors typically have blades with distinct handles, including one for the thumb—a lefty’s thumb will usually get stuck in the finger hole because they’re holding it upside-down. Fortunately, most operating rooms are equipped with scissors for both hands.

2. WRITING

A spiral notebook poses problems for a left-handed writer
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Because a lefty’s hand is running through everything being written, signatures, notes, and other scribblings often turn into a smeared mess. Writing in three-ringed binders or notebooks is even worse, since the spine makes it difficult to rest your hand against a smooth surface. The worst part? Gripping the pen cap with your left hand forces it to loosen up, making for a writing utensil that comes apart while you’re trying to use it.

3. HAVING DINNER COMPANY

If you know anyone who prefers to eat alone, ask about their dominant hand. It might be because using their left arm to dig into food means engaging in a constant battle for table real estate with a person on their left who is eating with their right arm. It also means their drinking glasses will be parked next to one another, with spillage always a looming threat.

4. WALKING

A man walks along a stretch of road
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Even sober, a lefty’s locomotion is affected. Why? Because when they cross paths with someone walking in the opposite direction, both tend to lean into their dominant side—putting them in front of each other yet again.

5. BANKING

To make sure their pens don’t wind up lost or stolen, most banks will tether them to a flimsy chain on the table. It’s non-invasive for right-handed people, but lefties are forced to try to sign checks with a chain constantly pulling against their hand movement.

6. PUTTING ON CLOTHES

A jeans zipper appears on the right side
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The fly on jeans, zippered coats, and other apparel usually opens on the right side, creating a barrier of entry for lefties. Buttons escalate the difficulty. Some women’s clothing reverses this, putting closures on the left. The tradition is thought to have started when servants would dress their charges in the Victorian era: Left-sided buttons would be to their right.

7. USING CELL PHONES

Although Apple is a prime culprit, many cell phones can be problematic for lefties. For one thing, cradling the device with your left hand can sometimes obscure the antenna, affecting reception. For another, control blocks can default to the right side in landscape mode, putting them out of reach.

8. MEASURING FOOD INGREDIENTS

A measuring cup that looks to be designed for right-handed use
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Glass or plastic measuring cups frequently print serving amounts to the left of the handle, meaning lefties who pour with their left and hold the cup with their right will either see nothing at all or the metric system side. 

9. HYDRATING AND DRIVING

Most lefties get used to shifting with their right hand, but it’s still awkward to try and fetch a (non-alcoholic) drink from the cup holder on the right side of the driver’s seat.

10. OPENING CANS

A can opener made for right-handed use
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Manual can openers favor right-handed operation, meaning lefties are forced to either obscure the knob with their left or move in the opposite direction. (Pull-tab cans have saved the sanity of many a lefty.) The same holds true for potato peelers, which are engineered for the right-handed majority. Fortunately, a few stores sell mirror-imaged kitchen tools.

11. PAINTING NAILS

Most day-to-day tasks can be modified or at least tolerated by lefties, but those who opt to paint their nails find that their left hand winds up a mess. The same is true for right-handed people, too—all the better to give them a taste of lefty life.

11 Sharp Facts About Annie Oakley

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Getty

You probably know that Annie Oakley was an outstanding sharpshooter who became famous while performing in Buffalo Bill’s Wild West Show. But if your knowledge of her life is limited to Annie Get Your Gun, we’ve got you covered. In honor of her birthday, here are 11 facts about Oakley, the Little Sure Shot of the Wild West.

1. SHE MADE HER FIRST SHOT AT 8 YEARS OLD.

Born on August 13, 1860 in a rural part of western Ohio, Phoebe Ann Moses grew up poor. Her father’s death in 1866 meant that she had to contribute to help her family survive, so she trapped small animals such as quail for food. At eight years old, she made her first shot when she killed a squirrel outside her house. “It was a wonderful shot, going right through the head from side to side. My mother was so frightened when she learned that I had taken down the loaded gun and shot it that I was forbidden to touch it again for eight months,” she later said.

2. SHE USED HER SHOOTING SKILLS TO PAY OFF HER MOM’S MORTGAGE.

Despite Oakley’s top-notch shooting skills, her widowed mother struggled to make ends meet. She sent Oakley to work for another family in exchange for her daughter getting an education. As a teenager, Oakley returned home (after working as a servant for an abusive family) and continued to hunt animals. She sold the meat to an Ohio grocery store, earning enough money to pay her mom’s $200 mortgage. She later wrote: "Oh, how my heart leaped with joy as I handed the money to mother and told her that I had saved enough to pay it off!"

3. SHE BEAT HER FUTURE HUSBAND IN A SHOOTING MATCH.

At 15 years old, Oakley participated in a shooting match on Thanksgiving with Frank Butler, an Irish-American professional marksman. The match, which happened in Cincinnati, was a doozy. To Butler’s surprise, the teenage girl outshot him by one clay pigeon, and he lost the $100 bet he had placed. Rather than feel embarrassed or emasculated by his loss, Butler was impressed and interested, and the two married the following year.

4. DESPITE HER PROFESSION, SHE EMPHASIZED HER FEMININITY.


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At the end of the 19th century, shooting was a predominantly male activity, and Oakley certainly stood out. But rather than dress or behave like a man to fit in, she emphasized her femininity. She wore her own homemade costumes on stage, behaved modestly, and engaged in "proper" female activities such as embroidery in her spare time.

5. SHE WAS ONLY FIVE FEET TALL.

In addition to Oakley’s gender, her diminutive stature made her stand out in the world of sharpshooting. In 1884, the Sioux chieftain Sitting Bull befriended Oakley when the two performers were traveling across the country. Acknowledging both her height and her shooting skill, Sitting Bull nicknamed Oakley Watanya Cicillia (English translation: Little Sure Shot). The American Indian warrior liked Oakley so much that he gave her his special moccasins to "adopt" her as his daughter.

6. SHE PERFORMED FOR KINGS AND QUEENS IN EUROPE.


Wikimedia Commons, Public Domain

Although the concept of the Wild West is firmly rooted in Americana, Oakley showed off her shooting skills across Europe as part of Buffalo Bill’s Wild West show. In 1887, she performed for Queen Victoria at the American Exposition in London, and the queen reportedly told Oakley that she was a "very clever little girl." In 1889, Oakley performed at the Paris Exposition and traveled to Italy and Spain. The press loved her, the king of Senegal wanted her to come help control the tiger population in his country, and Italy’s King Umberto I was a fan.

7. SHE OFFERED TO LEAD FEMALE SHOOTERS IN WORLD WAR I.

Wanting to use her shooting skills to serve her country, Oakley wrote a letter to President McKinley in 1898. She offered to provide 50 female sharpshooters (with their own arms and ammunition) to fight for the United States in the Spanish-American War, but she never got a response. Similarly, in 1917, she contacted the U.S. Secretary of War to offer her expertise to teach an army unit of women shooters to fight in World War I. She didn’t hear back, so she visited army camps, raised money for the Red Cross, and volunteered with military charities instead.

8. SHE SUED THE PRESS FOR PUBLICIZING HER (NONEXISTENT) DRUG ADDICTION.

In August 1903, two of William Randolph Hearst’s newspapers in Chicago reported that Oakley was a cocaine addict who was arrested for stealing a black man’s pants. Other newspapers ran the story, and Oakley—who was neither a drug addict nor a thief—was horrified. "The terrible piece … nearly killed me … The only thing that kept me alive was the desire to purge my character," she said.

The woman who had been arrested in Chicago was a burlesque performer whose stage name was Any Oakley. Most newspapers published retractions, but Hearst didn’t. He (unsuccessfully) hired a private investigator to uncover anything sordid about Oakley. Oakley sued 55 newspapers for libel, ultimately winning or settling 54 of them by 1910. Despite winning money from Hearst and other newspapers, costly legal expenses meant that she ultimately lost money to clear her name.

9. THANKS TO THOMAS EDISON, SHE BECAME A FILM ACTRESS.

In 1888, Oakley acted in Deadwood Dick, a financially unsuccessful play. At the Paris Exposition the next year, though, she met Buffalo Bill Cody’s friend Thomas Edison. In 1894, Oakley visited Edison in New Jersey and showed off her shooting skills for the inventor’s Kinetoscope. The resulting film, called The Little Sure Shot of the Wild West, featured Oakley shooting a rifle to break glass balls. Although she didn’t continue acting in film, she did act in The Western Girl, a play in which she portrayed a sharpshooter, in 1902 and 1903.

10. TWO SERIOUS ACCIDENTS HALTED HER CAREER.


Annie Oakley in 1922

Wikimedia Commons, Public Domain

In 1901, Oakley was injured in a train accident while traveling between North Carolina and Virginia for a performance. Although reports differ about the severity of her injuries, we do know that she took a year off from performing after the accident. Two decades later, Oakley was injured in a car accident in Florida. Her hip and ankle were fractured, and she wore a leg brace until 1926, when she passed away from pernicious anemia in Ohio at age 66. Frank Butler, her husband of 50 years, died 18 days later.

11. HER NAME BECAME AN IDIOMATIC EXPRESSION.

You know you’ve made it when your name becomes an idiom. Because of her shooting skills, the phrase "Annie Oakley" acquired a meaning of a free ticket to an event. Performing with Buffalo Bill’s Wild West show, Oakley shot holes in tiny objects, making targets out of everything from playing cards to a dime to a cigar dangling out of her husband’s mouth. Because free admission tickets for theatrical shows had holes punched in them (so they wouldn’t be sold to someone else), these tickets came to be called "Annie Oakleys."

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