CLOSE
V via Flickr // CC BY-NC 2.0

# The Homemaker Who Helped Solve One of Geometry's Oldest Puzzles

V via Flickr // CC BY-NC 2.0

The next time you find yourself staring at your bathroom floor tiles, thank Marjorie Rice. The San Diego homemaker helped solve one of the oldest problems in geometry: figuring out which shapes could "tile the plane," or seamlessly cover a flat surface in an endless, repeating pattern. Rice's hand-drawn doodles in the 1970s led to major discoveries in the last few years, finally answering the puzzle that had stumped classical thinkers.

Ancient Greek mathematicians believed that certain shapes could tile the plane, without overlapping or leaving any gaps, in a pattern called a tessellation. They proved that all triangles and quadrilaterals, and some convex hexagons (six-sided shapes), could tile the plane. But for centuries, no one knew how many tiling convex pentagons (irregular five-sided shapes) were out there.

The hunt for tiling pentagons began in 1918 when German mathematician Karl Reinhardt described the first five types of tessellating pentagons. For 50 years it was believed that he had found them all, but in 1968, physicist R. B. Kershner discovered three more classes. Richard James, a computer scientist in California, found another in 1975, bringing the total to nine.

That year, Rice read a column by Martin Gardner in Scientific American about the research and began experimenting to find more tiling pentagons. "I became fascinated with the subject and wanted to understand what made each type unique," Rice wrote in an essay about M.C. Escher's use of repeating patterns. "Lacking a mathematical background, I developed my own notation system and in a few months discovered a new type which I sent to Martin Gardner. He sent it to Doris Schattschneider to determine if it truly was a new type, and indeed it was."

Schattschneider, a mathematics professor at Moravian College in Bethlehem, Pennsylvania, deciphered Rice's notation and realized she had found four new types—more than anyone other than Reinhardt. Schattschneider helped formally announce Rice's discoveries in 1977.

"My dad had no idea what my mom was doing and discovering," her daughter Kathy Rice told Quanta Magazine.

It took another eight years for the next type of tiling pentagon to be found, this time by University of Dortmund mathematician Rolf Stein. Then the trail went cold for 30 years.

In 2015, mathematicians Jennifer McLoud-Mann, Casey Mann, and David von Derau at the University of Washington, Bothell, found the 15th class of tessellating pentagon using a supercomputer. Then, in July 2017, French mathematician Michaël Rao completed the classification of all convex polygons, including pentagons, that can tile the plane. He confirmed that only the 15 known convex pentagons could tessellate [PDF].

The immense amount of research and the scale of the recent discoveries makes the achievements of Marjorie Rice all the more impressive. Though she lacked more than a high-school education and access to supercomputers, Rice remains the most prolific discoverer of tiling pentagons to emerge in the century since Reinhardt first attempted to crack the problem.

Chemung County Historical Society, Elmira, NY
arrow
History
John W. Jones: The Runaway Slave Who Buried Nearly 3000 Confederate Soldiers
Chemung County Historical Society, Elmira, NY

John W. Jones was as close to a sinless man as you could find—with the exception of the time he lied to his mother.

It was a late June evening in 1844 and the 26-year-old enslaved man, who lived on a plantation near Leesburg, Virginia, told his mother that he was leaving to attend a party. His real plans were much riskier. Jones slipped outside, grabbed a pistol, and rendezvoused with four other enslaved men. With starlight as their guide, they crept through the Virginia woods. Their destination: North.

The men hiked approximately 20 miles every day, dodging slave catchers in Maryland and crossing the Mason-Dixon Line into the free state of Pennsylvania. Following a major route along the Underground Railroad, they needled through Harrisburg and Williamsport and traced a path along what is now State Route 14. When the exhausted men snuck into a barn near the New York border to sleep, Jones kept guard as the others rested: He sat down, laid a shotgun on his lap, and kept his eyes peeled.

“He was serious about getting his freedom,” says Talima Aaron, President of the John W. Jones Museum Board of Trustees. “He understood the danger, and he constantly took responsibility for others. You’ll notice that was a thread for him—responsibility for others.”

Jones never had to use the gun. When the barn’s owner, Nathaniel Smith, discovered the five men on his property, he invited them into his home. His wife Sarah served the group hot biscuits and butter and cared for them until their strength returned. It was the first time many of them had ever been inside a white person’s home. According to an 1885 profile in The Elmira Telegram, the gesture brought the men to tears.

On July 5, 1844, Jones crossed a toll bridge into Elmira, New York, with less than \$2 in his pocket. Unlike most runaways bound for Canada, Jones decided to stay in Elmira. It’s here that Jones would become one of the country's most successful Underground Railroad conductors, one of the richest black men in the state of New York, and the last earthly link for nearly 3000 dead Confederate soldiers.

Living in the north did not mean Jones had it easy. He could not vote. He still shared sidewalks with former slave-owners. When he asked to receive an education at the local schools, he was denied.

But Jones had a knack for cracking ceilings. After earning the admiration of a local judge, he was allowed to study at an all-women’s seminary, exchanging janitorial work for reading and writing lessons. He joined a church with abolitionist leanings and become its sexton, maintaining its cemetery. Then he became the sexton of a second cemetery, and then a third. The community quickly grew to respect his work ethic and, eventually, Jones had earned enough money to buy a small house—a house that he transformed into a vital hub for the Underground Railroad.

At the time, the Underground Railroad—an informal network of trails, hiding places, and guides that helped slaves escape northward—was under intense scrutiny. The 1850 Fugitive Slave Act had created financial incentives to report runaways living in free states. “Slave catchers from the south could come up to a place like Elmira and claim that a person of color was a runaway slave, and they could haul them back into slavery—even if that person had been born free,” says Bruce Whitmarsh, Director of the Chemung County Historical Society. There were steep penalties for aiding a person’s escape.

Jones didn’t care. Not only did he join the Underground Railroad, he was openly vocal about it, loudly pledging his opposition to the Fugitive Slave Act in a message that was published in abolitionist newspapers across the region: “Resolved, that we, the colored citizens of Elmira, do hereby form ourselves into a society for the purpose of protecting ourselves against those persons, (slave-catchers) prowling through different parts of this and other States.” Jones committed to resisting the law, even at the risk that “everyone of us be assassinated.”

The Underground Railroad in Elmira was unique: Since the town included the only train stop between Philadelphia and Ontario, it actually involved locomotives. Jones communicated regularly with William Still, the chief "conductor" of the Underground Railroad in Philadelphia, and built a cozy network of abolitionists who worked on trains passing through town. He provided runaways with housing, food, and even part-time jobs. “Runaways usually came in groups of four, six, or 10,” Aaron says. “But he had up to 30 at once in his little house.” Jones arranged hiding space for all of the escapees on the 4 a.m. “Freedom Baggage Car” to Canada, as it was unofficially known.

Over the course of nine years, Jones aided the escape of around 800 runaway slaves. Not one was captured.

During the last years of the Civil War, the same railroad tracks that had delivered hundreds of runaways to freedom began to carry thousands of captive Confederate soldiers to Elmira’s new prisoner of war camp. Once again, Jones would be there.

Of the 620,000 Civil War deaths, approximately 10 percent occurred at prison camps. The most notorious P.O.W. camp—in Andersonville, Georgia—saw 13,000 Union troops, or approximately 29 percent of the prison population, perish. After the war, Andersonville's commander was tried for war crimes. The camp is now a National Historic Site.

Meanwhile, the prison camp in Elmira has been largely forgotten. Today, the riverside site is little more than an unremarkable patch of dandelion-speckled grass; a small, easy-to-miss monument is the only marker. It belies the fact that while Elmira's camp was noticeably smaller than Andersonville's—only one-quarter its size—it was just as deadly: If you were a prisoner at “Hellmira,” there was a one-in-four chance you would die.

Chemung County Historical Society, Elmira, NY

Elmira was never supposed to have a prison camp; it was a training depot for Union soldiers. But when the Confederacy began refusing to exchange African-American soldiers—who it considered captive slaves, not prisoners of war—the Union stopped participating in prisoner exchanges. “Both sides started scrambling for places to expand, and that’s how Elmira got caught up in the web,” says Terri Olszowy, a Board Member for the Friends of the Elmira Civil War Prison Camp.

The rollout was ill-planned, Olszowy explains. When it opened in July 1864, the camp had no hospital or medical staff. The first prisoners were already in rough shape and deteriorated quickly. Latrines were placed uphill from a small body of water called Foster’s Pond, which quickly became a cesspool. A shelter shortage meant that hundreds of soldiers were still living in tents by Christmas. During spring, the Chemung River flooded the grounds. Rats crawled everywhere. When authorities released a dog to catch them, the prisoners ate the dog.

The camp grew overcrowded. Designed to hold only 5000 prisoners, it saw approximately 7000 to 10,000 men confined there at its peak. Across the street, an observation tower allowed locals the opportunity to gawk at these prisoners through a pair of binoculars. It cost 10 cents.

It must have been a depressing sight, a scene of men stricken with dysentery, scurvy, typhoid, pneumonia, and smallpox. Many prisoners attempted to escape. One group successfully dug a 66-foot tunnel with spoons and knives. One man fled by hiding in a barrel of swill. Another hid inside a coffin, leaping out as he was being hauled to Woodlawn Cemetery.

It’s said that 2973 Confederate prisoners left the Elmira prison camp in coffins for real. The job to bury them belonged to the town’s sexton: John W. Jones.

The P.O.W. cemetery in Elmira is unique. The dead at many prison camps were buried in mass graves; Chicago’s Oak Woods Cemetery, for example, contains a plot filled with the remains of prisoners detained at Camp Douglas that is believed to be largest mass grave in the western hemisphere. All 2973 of the dead at Elmira, however, received an individual, marked grave in a special section of Woodlawn cemetery. Only seven are unknown. Jones's effort to give each soldier an individual grave, as well as his meticulous record-keeping, were a big part of why the federal government designated the P.O.W. portion of Woodlawn a "National Cemetery" in 1877—a status awarded to veterans' cemeteries deemed to be of national importance, and which has only been awarded to 135 cemeteries nationwide.

Jones treated each dead soldier with superhuman levels of grace. Overseeing a crew of 12, he managed the burial of about six soldiers every day, treating each body as if that person had been a member of his own church. He kept detailed records of each soldier’s identity by creating improvised dog tags: Around each person's neck or under their arm, Jones tucked a jar containing a paper detailing their name, rank, and regiment. That same information was neatly scrawled on each coffin. When the dirt settled, Jones marked each plot with a wooden headstone.

“No one told him how to do that job, he did it in the way that he thought was right—even though the people he buried were fighting a war to keep people like him enslaved,” Aaron says. “He even knew one of the young men who had died, and he reached back to the South and told the parents so they knew where their child was buried. That speaks to his compassion.”

According to Clayton W. Holmes’s 1912 book Elmira Prison Camp, “History does not record anything to challenge the assertion that at no prison, North or South, were the dead so reverently cared for, or a more perfect record kept.” In fact, when representatives of the Daughters of the Confederacy came to Elmira at the turn of the century to consider repatriating the remains, Jones’s handiwork convinced them to touch not a blade of grass. Instead, a monument in the cemetery commemorates the “honorable way in which they were laid to rest by a caring man.”

Aaron sees a second moral in the story. “People always talk about the tension between him being an escaped slave and burying with respect and dignity these Confederate soldiers fighting to keep people like him as slaves,” she says. “But to me there’s a subtext: Here is a grown man who escaped slavery, and the first thing he wanted to do when he reached freedom was get an education. Because of that, he was able to keep these meticulous records that later led to this national designation: It became a historical moment because this man, who was denied an education, got one.”

Chemung County Historical Society, Elmira, NY

It also made a mark on Jones’s bank account. Jones earned \$2.50 for each soldier he buried. It wasn’t much, but by the time he had finished burying nearly 3000 Confederate dead, he had become one of the 10 richest African-Americans in the state of New York. With that money, he bought a handsome farm of at least 12 acres.

It was a bittersweet purchase. Not only is it believed that parts of his home were built from wooden scraps of the disassembled Elmira prison camp, Jones had purchased the home when New York state law stipulated that black men must own \$250 worth of property in order to vote. His home—today listed on the National Register of Historic Places [PDF]—earned Jones that right to vote.

For the remainder of his life, Jones continued working as a sexton and church usher. In 1900, he died and was buried in one of the cemeteries that had become his life’s work.

Incidentally, his death also marked the end of a local mystery: For nearly two decades, fresh flowers kept appearing on the freshly manicured grave of a woman named Sarah Smith. Nobody knew why the flowers appeared there or where they originated—until the decorations stopped appearing immediately after Jones’s death. Residents later realized that the grave belonged to the same Sarah Smith who, 56 years earlier, had invited John W. Jones and his friends into her home for butter, biscuits, and a good night’s rest.

Jennifer Young, AFP/Getty Images
arrow
TBT
An Affair to Dismember: John Wayne Bobbitt's Penis at 25
Jennifer Young, AFP/Getty Images

In the early morning hours of June 23, 1993, Manassas, Virginia manicurist Lorena Bobbitt crept into the bedroom she shared with her husband, John Wayne Bobbitt. While John—who had been drinking heavily—slept, she proceeded to mutilate his genitals with a 12-inch kitchen knife. When a drunken John woke up, the sheets were covered in blood; Lorena ran to her car, knife and lump of flesh in tow. Not quite sure what to do next, she wound up tossing part of his shaft out the window.

The scene was so morbid and so titillating that the news media couldn’t get enough. From the time Lorena performed the amputation to her acquittal seven months later, the story of a marriage so broken it ended in genital disfigurement ran almost around the clock.

But reporters had a major hurdle to clear: The word penis had never been printed or spoken aloud with any regularity in American news coverage.

They tried euphemisms, i.e. male member, appendage. When those ran out, The New York Times finally acquiesced and began using “penis” in their coverage of the criminal trial. According to journalist Gay Talese, the sheer volume of the Bobbitt circus broke one of the last sexual taboos in mainstream culture. Soon after, the word penis began regularly appearing on late night talk shows and in print.

There was really no other choice. While the Bobbitt case raised issues over domestic violence, female empowerment, and even the threshold for celebrity, the story always boiled down to that one lurid moment. John Wayne’s reattached, mostly functional penis was—and perhaps still is—the most famous sexual organ in America.

John Wayne and Lorena first met in 1988, when the burly 21-year-old Marine walked into a club for enlisted men near Quantico in Virginia and spotted the then-19-year-old, who was born in Ecuador and raised in Venezuela. They married just months later and settled in Manassas, where Lorena worked in the beauty industry and John Wayne worked as a cab driver and bar bouncer. Friends and relatives of the couple who would later be questioned on the witness stand described a tumultuous coupling, one that saw the two separated briefly in 1991 before reconciling.

John Wayne was temperamental and physical with Lorena, a fact that her eventual prosecutors would later admit. Divorce was on the table when John Wayne came home the night of June 23, 1993 and when, Lorena alleged, he raped her. (In a separate trial, a jury found John Wayne not guilty of martial sexual abuse in the five days preceding the attack.) After falling asleep, he awoke to a mutilated penis, his wife having excised an inch or more of its lower third portion.

Police retrieved the missing flesh and handed it over to emergency doctors. Before being wheeled in for a nine-hour operation to reattach the severed portion, John Wayne said he considered suicide.

Pool/AFP/Getty Images

The surgery was more or less successful—John Wayne later recollected calling his mother and enthusiastically telling her he had gotten his first post-operative erection—but attempts to have Lorena convicted for the attack were not. In January 1994, a jury found her not guilty by reason of temporary insanity. The defense argued that Lorena had been so traumatized by abuse that she acted irrationally but not maliciously.

The trial and its outcome seemed to provide metaphorical fuel for ever-present issues regarding gender. Although he had not technically been castrated, John Wayne was certainly emasculated, and in a rather horrific way—punishment, some believed, for his deplorable behavior. In defacing his manhood, Lorena seemed to become emblematic of what some women felt like doing to spousal abusers.

Lorena fielded book, movie, and interview offers but largely stayed out of the spotlight, reverting to her maiden name and trying to disappear. (She was also sentenced to a 45-day psychiatric evaluation to make sure she presented no danger to the public.) It was John Wayne who perpetuated his own celebrity, turning what was a gruesome assault into a story worth monetizing.

First, there was the requisite appearance on The Howard Stern Show in December 1993—one of many—in which Stern attempted to fundraise for Bobbitt’s \$250,000 in medical and legal expenses.

Stern and other interviewers were preoccupied with Bobbitt’s sexual ability. As of that December, Bobbitt told Stern, he had not been able to engage in any intercourse; he claimed his penis bore little evidence of the attack aside from a “slight” scar; it hurt a little when he showered. He urinated with use of a catheter for two months following the procedure.

The radio panhandling met with some success, although as some observers noted virtually from the beginning, Bobbitt’s opportunities to cash in on his notoriety were almost inevitably in the red light district of the entertainment industry. In 1994, he signed a deal for \$1 million to appear in an adult video distributed by Leisure Time Communications titled John Wayne Bobbitt: Uncut. A kind of pornographic biopic, Bobbitt played himself, reenacting the attack and then proving his restored sexual abilities by engaging in sexual acts with a succession of actresses. In what must be one of the few adult movie reviews published by Entertainment Weekly, critic Owen Gleiberman observed that Bobbitt’s reconstructed penis had “no real stitch marks” but looked as though it “may have lost an inch or two.”

Uncut was a curiosity, but Bobbitt was unable to sustain interest in two follow-up tapes: One was titled Frankenpenis and may have lived up to a viewer’s anticipation of a freakish member, due to a penis enlargement surgery John Wayne underwent following the release of the first video.

Having exhausted his potential in pornography, Bobbitt and his penis sought other venues. First, he tried his hand at stand-up comedy. When that failed to pan out, Dennis Hof, owner of the Bunny Ranch brothel, paid him \$50,000 a year to be a bartender/chauffeur/handyman

, not unlike the way aging boxing legends like Joe Louis used to stand near casino doors so patrons could shake the hand of a champion.

At the Ranch, Bobbitt introduced himself to men waiting for prostitutes and sometimes indulged their request to have him drop his pants for a look. Hof didn’t keep him on for long, later calling him a “stupid, low-life creep” and “boring oaf” who couldn’t keep his hands off of Hof’s female employees.

J. David Ake, AFP/Getty Images

Bobbitt later found a brief home in a carnival, alongside a professional insect eater and a man with a split tongue. Here, too, Bobbitt seemed to fail in realizing his potential, refusing to be a target for a knife-thrower or learn the art of hammering nails into his nose.

He also appeared to have learned little from the consequences of his boorish behavior. In 1999, he was jailed for pushing a girlfriend into a wall. In 2005, he was arrested and charged with battery in relation to an incident involving his new wife, Joanna Ferrell, the third such allegation during their now-defunct marriage. (He was later acquitted.) The accusations cost him a gig facing off against Joey Buttafuoco on Fox’s Celebrity Boxing.

Currently, Bobbitt has settled in Niagara Falls and works as a limo driver and carpenter. Lorena has founded Lorena’s Red Wagon, an organization offering assistance to women victimized by domestic violence. Lorena’s actions in 1993 were largely unmatched until 2011, when a California woman named Catherine Kieu took a knife and severed her husband’s penis following an argument.

The man would not have an opportunity for a Bobbitt-esque reattachment and subsequent victory lap. Perhaps learning from Lorena’s mistake, Kieu didn't merely toss the severed flesh away. She pulverized the penis in their garbage disposal.

### SECTIONS

arrow
LIVE SMARTER
arrow
LIVE SMARTER
More from mental floss studios