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

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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.

# 10 Surprising Facts About Ernest Hemingway

Picture Post/Hulton Archive/Getty Images

Ernest Hemingway was a titan of 20th-century literature, converting his lived experiences in multiple wars into rich, stirring tales like A Farewell to Arms and For Whom the Bell Tolls. The avid sportsman also called upon his love for the outdoors to craft bittersweet metaphorical works like Big Two-Hearted River and the Pulitzer Prize-winning The Old Man and the Sea. Here are 10 facts about the writer known as Papa, who was born on July 21, 1899.

## 1. Ernest Hemingway earned the Italian Silver Medal of Valor and a Bronze Star.

Hemingway served as an ambulance driver in Italy during World War I, and on July 8, 1918, he was badly wounded by mortar fire—yet he managed to help Italian soldiers reach safety. The action earned him an Italian Silver Medal of Valor. That honor was paralleled almost 30 years later when the U.S. awarded him a Bronze Star for courage displayed while covering the European theater in World War II as a journalist. His articles appeared in Collier’s and other magazines.

## 2. Ernest Hemingway was also accused—and cleared—of war crimes.

Following D-Day on June 6, 1944, when Hemingway, a civilian, was not allowed to disembark on Omaha Beach, he led a band of Resistance fighters in the French town of Rambouillet on a mission to gather intelligence. The problem was, war correspondents aren't supposed to lead armed troops, according to the Geneva Convention. The Inspector General of the Third Army charged Hemingway with several serious offenses, including removing patches from his clothing that identified him as a journalist, stockpiling weapons in his hotel room, and commanding a faction of Resistance operatives. Eventually, he was cleared of wrongdoing.

Hemingway always maintained that he’d done nothing but act as an advisor. He wrote to The New York Times in 1951, stating he “had a certain amount of knowledge about guerilla warfare and irregular tactics as well as a grounding in more formal war, and I was willing and happy to work for or be of use to anybody who would give me anything to do within my capabilities.”

## 3. Gertrude Stein was godmother to Ernest Hemingway's son, Jack.

Renowned American modernist writer Gertude Stein moved to Paris in 1903 and hosted regular salons that were attended by luminaries and artists of the time. They included Pablo Picasso, Ezra Pound, F. Scott Fitzgerald, and a young Ernest Hemingway. Stein became godmother to Hemingway’s first son, Jack, in 1923.

## 4. Ernest Hemingway was allegedly a KGB spy—but he wasn't very good at it.

When Collier's sent the legendary war correspondent Martha Gellhorn to China for a story in 1941, Hemingway, her husband, accompanied her and filed dispatches for PM. Documentation from the Stalin-era KGB (revealed in a 2009 book) shows that Hemingway was possibly recruited as a willing, clandestine source just prior to the trip and was given the codename “Argo.” The documents also show that he didn’t deliver any useful political intel, wasn’t trained for espionage, and only stayed on their list of active sources until the end of the decade.

## 5. Ernest Hemingway checked out F. Scott Fitzgerald's penis in the men's room.

Hemingway chronicled his life in Paris in his 1964 memoir A Moveable Feast, and revealed one notorious encounter with the Great Gatsby author in the book. Fitzgerald remarked that his wife Zelda has mocked his manhood by claiming he wouldn't be able to satisfy a lover. Hemingway suggested he investigate for himself. He took Fitzgerald to the bathroom at Michaud's, a popular restaurant in Paris, to examine his penis. Hemingway ultimately told his friend that his physical endowment was of a totally normal size and suggested he check out some nude statues at the Louvre for confirmation.

## 6. One of Ernest Hemingway's best works came about from him leaving some luggage at the Ritz Hotel in Paris.

Speaking of A Moveable Feast, Hemingway wrote it later in life (it was published posthumously) after a 1956 stay at the Ritz Hotel in Paris wherein he was reminded that he’d left a steamer trunk (made for him by Louis Vuitton) in the hotel’s basement in 1930. When he opened it, he rediscovered personal letters, menus, outdoor gear, and two stacks of notebooks that became the basis for the memoir of his youth in Paris's café culture.

## 7. The famous "Baby Shoes" story is most likely a myth.

Oddly enough, a story many people associate with Hemingway probably has nothing to do with him. The legend goes that one night, while drinking, Hemingway bet some friends that he could write a six-word short story. Incredulous, they all put money on the table, and on a napkin Hemingway wrote the words “For Sale: Baby Shoes, Never Worn.” He won the bet. Unfortunately, there’s no evidence it ever happened. Some newspapers had printed versions of the six-word plotline in the 1910s without crediting Hemingway, and there's no record of his link to the phrase until 1991 (in a book about the publishing business), three decades after Hemingway’s death.

## 8. Ernest Hemingway almost died in back-to-back plane crashes.

In 1954, Hemingway and his fourth wife, Time and Life correspondent Mary Welsh, were vacationing in Belgian Congo when their sightseeing charter flight clipped a utility pole and crashed. When attempting to reach medical care in Entebbe the following day, they boarded another plane, which exploded upon takeoff, leaving Hemingway with burns, a concussion, and his brain leaking cerebral fluid. When they finally got to Entebbe (by truck), they found journalists had already reported their deaths, so Hemingway got to read his own obituaries.

## 9. Ernest Hemingway dedicated a book to each of his four wives.

Each time he got divorced, Hemingway was married again within the year—but he always left something behind in print. The dedication for The Sun Also Rises went to his first wife, Elizabeth Hadley Richardson; Death in the Afternoon was dedicated to second wife Pauline Pfeiffer; For Whom the Bell Tolls was for third wife Martha Gellhorn; and Across the River and Into the Trees went “To Mary with Love.”

## 10. Ernest Hemingway's house in Key West features a urinal from his favorite bar.

Hemingway wrote several iconic works, including To Have and Have Not, at his house in Key West, Florida. It’s also where he converted a urinal from a local bar into a fountain. Local haunt Sloppy Joe’s was a favorite watering hole of the irascible author, so when the place went under renovation, Hemingway took one of the urinals as a memento, quipping that he’d already poured enough money into it to make it his.

# Richard Nixon Had a Speech Prepared In the Event That Apollo 11's Mission Failed

Neil Armstrong, Michael Collins, and Buzz Aldrin share a laugh with President Richard Nixon while aboard the USS Hornet on July 24, 1969.
Richard Nixon Foundation via Getty Images

In July 1969, the world watched as the crew of Apollo 11 successfully entered lunar orbit, landed, then blasted off and returned to Earth. At each step of the way there were dangers and NASA had backup plans in case something went terribly wrong—though there wasn't much NASA could do from 384,403 kilometers away. In 1999, William Safire discussed the speech he wrote for President Richard Nixon just in case the mission failed. From Safire's article:

The most dangerous part of the trip was not landing the little module on the moon, but in launching it back up to the mother ship. If that failed, Neil Armstrong and Buzz Aldrin could not be rescued. Mission Control would have to "close down communications" and, as the world agonized, let the doomed astronauts starve to death or commit suicide.

Nixon aides H. R. Haldeman and Peter Flanigan told me to plan for that tragic contingency. On July 18, 1969, I recommended that "in event of moon disaster . . . the President should telephone each of the widows-to-be" and after NASA cut off contact "a clergyman should adopt the same procedure as a burial at sea, commending their souls to 'the deepest of the deep,' concluding with the Lord's Prayer." A draft Presidential speech was included.

Here's a scan of the speech:

And here's the text:

IN EVENT OF MOON DISASTER:

Fate has ordained that the men who went to the moon to explore in peace will stay on the moon to rest in peace.

These brave men, Neil Armstrong and Edwin Aldrin, know that there is no hope for their recovery. But they also know that there is hope for mankind in their sacrifice.

These two men are laying down their lives in mankind's most noble goal: the search for truth and understanding.

They will be mourned by their families and friends; they will be mourned by their nation; they will be mourned by the people of the world; they will be mourned by a Mother Earth that dared send two of her sons into the unknown.

In their exploration, they stirred the people of the world to feel as one; in their sacrifice, they bind more tightly the brotherhood of man.

In ancient days, men looked at stars and saw their heroes in the constellations. In modern times, we do much the same, but our heroes are epic men of flesh and blood.

Others will follow, and surely find their way home. Man's search will not be denied. But these men were the first, and they will remain the foremost in our hearts.

For every human being who looks up at the moon in the nights to come will know that there is some corner of another world that is forever mankind.

This story has been updated for 2019.

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