# 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.

# History Vs. Bonus Episode: The Case of the Missing Colt .38

One morning in early April 1990, rangers at Sagamore Hill National Historic Site were walking past a display at the Old Orchard Museum when they noticed that something was amiss. The display contained Theodore Roosevelt’s uniform from his time with the Rough Riders in the Spanish-American War, as well as his Colt Model 1895 .38 caliber double-action revolver.

Or at least, the gun should have been there. But … it wasn’t.

Jake Rossen:
At the time, it was relatively simple just to lift the case up without setting any alarm and taking it.

That’s Jake Rossen, senior staff writer at Mental Floss.

Rossen: That's exactly what someone did.

This particular gun had a fascinating history, even before it landed in TR’s hands. It was manufactured in Hartford, Connecticut, in March 1895, and was sold to the U.S. government, after which it ended up on the battleship Maine, as ship property. It was still on board on February 15, 1898, when the ship exploded in Havana, Cuba. Hundreds of men lost their lives in the blast, which was blamed on the Spanish and helped to push America into the war.

The gun may have remained in a watery grave if not for TR’s brother-in-law, William S. Cowles, who was one of the commanding officers sent to Cuba after the explosion as salvage divers brought up what they could from the wreck.

Rossen: And one of those items was a Colt revolver. Knowing that TR was a weapons aficionado, he gave it to him as a gift.

When the Spanish-American War broke out in 1898, TR quit his job as assistant secretary of the Navy, signed up to fight, and shipped out to Cuba with his volunteer regiment. With him was the blue-barreled Colt with the checkered wood handle. Roosevelt used the weapon in the Battle of San Juan Heights.

Rossen: Apparently he was able to take aim and shoot at two enemies. One he missed; one, he later wrote, he hit, the man fell over and almost assuredly died. Roosevelt obviously treasured the weapon prior to using it. After he used it, undoubtedly he considered it probably even more significant.

Eventually, the gun was inscribed. On one side, it read “From the sunken battle ship Maine.” and on the other, “July 1st 1898, San Juan, Carried and used by Col. Theodore Roosevelt.

Rossen: He kept it in his personal possession until his death. And later on, when his property, his home, became a historic site and part of the National Park Service, it eventually, like a lot of his possessions, went on display.

Which brings us back to where we started: The empty display case at Sagamore Hill National Historic Site. I’m your host, Erin McCarthy, and in this bonus episode of History Vs., we’re going to explore this strange story, which I first found out about when I visited Sagamore Hill for the podcast. I knew immediately that we had to write about it, so I put Jake on the case.

McCarthy: So when something like this goes missing on national park land, what's the next step? What do they do?

Rossen: When a crime takes place in a national park or on a national park site, it's technically federal land. And so the government usually gets in touch with park rangers and they frequently pass it on to an investigative unit. And in this case the museum was able to reach out to park rangers who conducted an initial investigation and eventually it made its way to the FBI. The gun had actually been stolen once before back in the 1960s, and fortunately, whoever stole it seemed to get cold feet once they had taken it. The gun was found not far from the museum. It had been discarded. But this time was a little bit different in the sense that the museum really had no practical security features. There were no surveillance cameras. The glass case wasn't locked.

In fact, as one national park employee explained it to us, “The case could be lifted and the lock just popped open.”

Rossen: It wasn't going to be that difficult for someone determined to take the gun if they really wanted to.

McCarthy: So once the FBI got involved, where did they even start in the search for suspects?

Rossen: When stuff like this happens, investigators will often look at employees first. Because a lot of times this can be the result of an inside job. The FBI eventually realized that no employee was at fault.

With museum employees ruled out, and a security system being installed in the museum, the FBI began going to gun shows and approaching gun dealers to see if they had crossed paths with someone trying to sell the Colt. But they weren’t necessarily optimistic about finding the gun that way. The gun was really distinctive, and therefore hard to sell.

Rossen: I think they probably felt that whoever took it was probably taking it for their own personal collection. And in that case, obviously, there really weren't many leads to follow.

Which isn’t to say that the FBI didn’t get tips. They actually got a ton of them. In the time before the internet, they would get phone calls. When email came about, they got emails. And sometimes, the leads would be worth looking into.

Rossen: There was a rumor it had been seen in Europe. But really the only promising lead, which turned out really not to be promising at all, was the idea that a gun with the same serial number had turned up in a buyback program in Pennsylvania. But when they looked into it more thoroughly, they realized even though that gun had that same serial number, it was a different model gun. And so they were essentially back to square one. As the reward kept creeping up and eventually I think it reached somewhere around \$8,100 and there's still no concrete leads, there's no one being enticed by a monetary compensation. And once you get 10 or 12 years into the gun being missing, again, this was back in 1990, you know, I imagine the FBI eventually felt it was time to maybe put this on the back burner.

But, 15 years after the gun went missing, there was finally a break in the case—one that may have been made possible by a divorce.

We’ll be right back.

More than 15 years after Theodore Roosevelt’s Colt Revolver went missing from the Old Orchard Museum at Sagamore Hill, one of the park rangers began receiving phone calls from a man who said he knew where the gun was.

That wasn’t necessarily unusual—they had gotten many similar calls before. What was unusual was that the man kept calling. He wouldn’t give his name, but he said he knew where the gun was—that he’d seen it wrapped in a sweatshirt. He was able to describe its engravings. He said that he wanted it returned to the museum—but he didn’t want to get anyone in trouble.

Rossen: The park ranger tried to plead with him and even told him, "Look, just put it in a box and drop it in the mail and that'll be that." But he couldn't really get through to the guy. Eventually, though, I think the man realized that he had to do something with the gun and he agreed to make contact with the FBI.

The man who had been calling was named Andy, and he lived in Florida.

Rossen: It turns out he had been seeing a woman, and the woman, who knew that Andy was a history buff, approached him one day and said, "Look, I've got this gun, it belonged to Teddy Roosevelt and, you know, you might want to take a look at it." Essentially Andy came to realize it was stolen, came to realize that actually it didn't belong to his girlfriend, but her ex-husband and her husband had essentially kept it around the house, sometimes wrapped up in a sweatshirt, sometimes tucked under the seat of a car.

McCarthy: So basically if that woman and her husband had not gotten divorced, the gun might still be missing?

Rossen: It's very possible, yeah.

The FBI approached Andy and asked him to retrieve the gun from his girlfriend.

Rossen: Again, he wanted to drag his feet a little bit and was reluctant about revealing the identity of his girlfriend, but being the FBI, they were rather persuasive with him.

The gun was retrieved and authenticated, and in 2006—16 years after it disappeared—it was returned to Sagamore Hill. Eventually, it took its place back in a case in the museum, one that was now much more secure.

As for the man who took the gun—we’ll call him Anthony T. He was charged with misdemeanor theft, which perhaps feels like a light sentence for someone who took something that belonged to a former president.

Rossen: It's interesting because if you look at heists involving valuable items, rare items, paintings, things of that nature, the punishment can be pretty severe. With something like Roosevelt's gun, even though there's been valuations placed on it that reached into the hundreds of thousands, I don't know that there's any definitive way of placing a price on it. And additionally, the federal government doesn't really insure these kinds of things. It seems the prosecutors looked at Anthony T.'s situation and realized that he was not by any means a professional thief, a career criminal, and decided to really let him off rather easily. He got probation, he had to pay a fine, and he had to perform a fair amount of community service.

Though the gun is back where it belongs, questions still linger. No one seems to know why Anthony took the gun, although investigators have posited that it was an impulsive act.

Rossen: So Anthony T was at the museum, and saw the gun, saw that there really probably wasn't any employee around, saw that the case could be easily manipulated. And it was a crime of opportunity. Actually, one of the investigators essentially described it as a kind of artifact shoplifting; something done on impulse and obviously something he came to regret. I think the irony really is the fact that Anthony, when he was charged with a crime, was charged with violating the American Antiquities Act of 1906, which is basically a law stating that “Hey, you know, you can't steal government property, items, or historic artifacts.”

The president who signed the American Antiquities Act into law? Theodore Roosevelt.

We’ll be back in a couple of weeks with another bonus episode of History Vs.

##### Credits

History Vs. is hosted by me, Erin McCarthy. This episode was written by me, with fact checking by Austin Thompson.

The executive producers are Erin McCarthy, Julie Douglas, and Tyler Klang. The supervising producer is Dylan Fagan. The show is edited by Dylan Fagan and Lowell Brillante. If you want to find out more about this episode, and Theodore Roosevelt, visit MentalFloss.com/historyvs.

History Vs. is a production of iHeartRadio and Mental Floss.

# 20 Surprising Facts About King Tutankhamun

The burial mask of Egyptian King Tutankhamun.
Hannes Magerstaedt/Getty Images

If you can only name one Egyptian pharaoh, it’s likely King Tut. Born around 1343 BCE, Tutankhamun made history as the youngest known monarch to preside over the ancient Egyptian empire. But that wasn’t his only claim to fame. In life, King Tut made important political decisions; in death, he captivated the public’s fascination and ignited their interest in mummies.

The discovery of King Tut's pristine tomb in 1922 remains one of the most important moments in all of Egyptian archaeology. From his confusing lineage to his impact on pop culture, here’s what you need to know about King Tutankhamun.

## 1. King Tut’s parents were related.

Tutankhamun was likely inbred—something that wasn’t uncommon with royal families trying to maintain a “pure” bloodline throughout history. Around 2010, an analysis of DNA taken from the mummies of King Tut and his relatives revealed that the boy pharaoh’s parents had been brother and sister, but that discovery has since been disputed.

Tut’s father has been identified as the heretic Akhenaten, but the identity of his mother remains unknown. At least one archaeologist believes that Tut’s mother was actually Queen Nefertiti—Akhenaten's cousin, and one of his wives.

## 2. King Tut had an incestuous relationship of his own.

King Tut was married to a woman named Ankhesenamun, who was the daughter of Akhenaten and Nefertiti. That made her Tutankhamun’s half-sister—or his full sister, if the theory about Nefertiti being his mother is true.

King Tut fathered two daughters with his wife, but unfortunately, both children were stillborn. Their bodies were mummified and eventually interred in King Tut’s tomb with him. Ankhesenamun outlived Tutankhamun and possibly got married to the pharaoh Ay (Tut’s uncle) after Tut’s death.

## 3. King Tut became pharaoh at age 9.

As the grandson of the pharaoh Amenhotep II and the son of pharaoh Ankhesenamun, Tutankhamun was destined for the throne. He assumed his position as Egypt’s leader at the young age of 9, and ruled until his death 10 years later around 1324 BCE. It is believed that King Tut is the youngest pharaoh ever to rule over the ancient Egyptian empire. Because he was so young when he came into power, his uncle Ay was likely in charge during those early years.

## 4. King Tut reversed his father’s religious reforms.

King Tut didn’t need to do much to impress his subjects—his father, pharaoh Akhenaten, had been a disastrous ruler. Akhenaten changed the established religion to focus on the worship of one god, the sun deity Aten, which left him branded as a heretic. Akhenaten also moved the holy capital from Thebes to Amarna.

When Tut became pharaoh he undid his father’s changes and declared Thebes to be the religious center once again. This helped him earn the trust of his people during his brief reign.

## 5. King Tut changed his name.

Profile of a wooden statue of King Tutankhamun.
Hulton Archive/Getty Images

King Tut went by many names during his lifetime. He was born with the name Tutankhaten, which translates to “living image of Aten.” After he become pharaoh, he changed his name to Tutankhamun or “living image of Amun.” This change was a reflection of Tut’s devotion to the god Amun, whom his father had neglected in favor of the god Aten. Today, Tutankhamun is most commonly known as King Tut.

## 6. King Tut had health issues.

King Tut had a severe bone disease that left him disabled. He had a clubbed left foot, which made it hard for him to move around. In ancient art he is regularly depicted sitting down when engaging in physical activities like archery, whereas other pharaohs were always shown standing up in similar scenarios. It’s believed that Tut’s inbred lineage contributed to his physical issues. CT scans of his mummy showed that his left leg had been broken and infected, which may have contributed to his untimely death.

## 7. Experts used to suspect that King Tut had been assassinated.

King Tut’s mummy was discovered with a hole in its skull, leading some people to believe that the young pharaoh had been assassinated with a blow to the head. This theory has since been widely debunked by experts. It’s now suspected that the hole was either put there by embalmers when King Tut was being mummified or it was created when archaeologists first removed the mummy’s gold mask. It’s much more likely that the infection in his leg was the cause of his death.

## 8. A chariot accident may have contributed to King Tut’s death.

King Tutankhamun's burial chariot, which was discovered in the pharaoh's tomb.
Art Media/Print Collector/Getty Images

If King Tut did indeed die from a broken leg, the question still remains of how he broke his leg in the first place. According to one theory, the teen king died in a horrible chariot accident, which is why one side of his body—including his leg—was found crushed. The chariots used by royalty in ancient Egypt were small and light, allowing them to reach high speeds. Although there’s no evidence that chariots were used for racing during this period, they were used during war and for hunting rides.

## 9. King Tut wasn’t history’s only young pharaoh.

King Tut was likely the youngest pharaoh to lead Egypt, but not my much. Cleopatra became co-regent with her younger brother (and husband) Ptolemy XIII in 51 BCE when he was just 10 years old. Looking beyond ancient Egypt, there are many young monarchs from history who shave years off Tut’s age record. China, Russia, England, Spain, and France are just a few countries that have crowned “rulers” when they were babies.

## 10. King Tut’s successors tried to erase him from history.

While King Tut did a lot to reverse his father’s unpopular reforms during his lifetime, none of it did much to protect Tut’s legacy in the long run. His successors did their best to remove his wife, Ankhesenamun, from history—and the memory of Tutankhamun along with her.

Tut was buried quickly and in a small tomb normally reserved for private citizens, not one of the grander tombs meant for pharaohs. Because his tomb was out of the way, it remained untouched for centuries until it was rediscovered in 1922. Now King Tut is the most famous Egyptian pharaoh of all time.

## 11. King Tut's tomb was robbed—twice.

Crates are carried out of King Tutankhamun's tomb in 1923.
Hulton Archive/Getty Images

Before King Tut’s tomb was discovered by Howard Carter in 1922, it was visited by grave robbers. The first break-in took place shortly after Tutankhamun was laid to rest. Following that initial incident, there was rubble blocking the burial chambers, but it didn't take long for a second set of intruders to tunnel their way in. Carter found the tomb in shambles with entryways blocked off to provide further protection to Tutankhamun.

## 12. King Tut had three coffins.

Inside King Tut’s stone sarcophagus were three coffins: The outermost pair were made of gilded wood and the inner coffin was crafted out of solid gold. Over the head and shoulders of the mummy was the ornate gold death mask that many people associate with Tutankhamun. The mummy was placed inside the Russian nesting doll-style coffins, and everything was put inside a large quartzite stone sarcophagus with a pink granite top.

## 13. Some people think King Tut’s tomb is cursed.

King Tut’s tomb has inspired many legends since it was discovered decades ago. Because many people associated with the site have subsequently met with misfortune, stories have spread about its supposed curse. Some of the victims of this so-called curse include George Jay Gould, a financier who got sick after visiting the tomb in 1923, and George Herbert, 5th Earl of Carnarvon, who died of blood poisoning after funding the dig. This so-called curse has been blamed for more than a dozen deaths.

## 14. King Tut was entombed with a meteorite dagger.

The tomb of Tutankhamun contained many extraordinary objects, one of which was a dagger carved from a meteorite. The dagger was found on the body of the mummy when he was discovered, but it wasn’t until a few years ago that portable x-ray ﬂuorescence spectrometry revealed that the materials came from space. The iron in the blade contained 10.8 percent nickel and .58 percent cobalt. Such a high nickel percentage indicated that the iron came from a meteorite, not Earth.

## 15. There are no hidden rooms in King Tut’s tomb.

Archaeologists surrounding sarcophagus in King Tut's tomb.
Ben Curtis, AFP/Getty Images

Even after it was excavated, King Tut’s tomb continued to capture the imaginations of archaeologists. In 2015, a British archaeologist put forth a theory based on laser scans that a second room was hidden behind a wall of the tomb and waiting to be explored. He even suggested that Tutankhamun’s stepmother, Queen Nefertiti, might be entombed there. That idea was put to rest when a comprehensive ground-penetrating radar survey showed there were no hidden rooms or corridors adjacent to the tomb.

After surviving 3000 years in a tomb in Egypt, King Tut’s iconic gold death mask was badly damaged when, around 2014, the mask’s braided beard broke off, and museum curators used epoxy glue to reattach it. This improvised solution may have ended up causing more lasting damage than the accident itself. Epoxy glue is hard to remove, and attempts to scrape off the adhesive resulted in permanent scratch marks on the artifact’s priceless gold face.

## 17. King Tut was buried with an ancient board game.

The ancient board game senet.
Dmitry Denisenkov via Flickr // CC BY-SA 2.0

One of the world’s oldest board games was discovered inside King Tut’s tomb. Senet, or “passing,” had been played in Egypt for 1800 years prior to Tutankhamun’s death. It was played by people of all class levels, and though the exact rules have been lost to time, it’s believed to have something to do with life and death. It even may have been an early version of backgammon.

## 18. King Tut rocked pop culture.

When his tomb was discovered in the early 20th century, King Tut had a massive impact on pop culture. The Egyptian aesthetic infiltrated the 1920s, appearing in fashion, home design, and architecture. Americans especially were so fascinated by King Tut that president Herbert Hoover even went so far as to name his dog after the young monarch. Tut’s impact was felt for decades after his discovery. The historical figure has been depicted countless times in movies, songs, and television shows.

## 19. King Tut’s tomb recently received a makeover.

English Egyptologist Howard Carter examines the golden sarcophagus of King Tutankhamun in Egypt in 1923.
Harry Burton/Apic/Getty Images

After years of traffic from tourists, King Tut’s tomb closed to visitors in 2009 to undergo a long conservation project. At the beginning of 2019, the archaeological site finally reopened to the public. Today, the attraction features an air filtration and ventilation system, restored wall paintings, a viewing platform, and new barriers to protect precious artifacts from viewers. King Tut’s tomb is one of the most popular destinations for tourists visiting Egypt.

## 20. We may finally know what King Tut really looked like.

By conducting a virtual autopsy of his mummy with CT scan data, scientists were able to build a 3D model of what King Tut may have looked like when he was alive 3000 years ago. The computer-generated image looks much different than the striking face depicted on Tut’s iconic gold mask. Rather than the god-like figure that’s been shown countless times in pop culture, Tutankhamun was a frail, ordinary teenager in reality.

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