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

V via Flickr // CC BY-NC 2.0
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.

On This Day in 1953, Jonas Salk Announced His Polio Vaccine

Getty Images
Getty Images

On March 26, 1953, Dr. Jonas Salk went on CBS radio to announce his vaccine for poliomyelitis. He had worked for three years to develop the polio vaccine, attacking a disease that killed 3000 Americans in 1952 alone, along with 58,000 newly reported cases. Polio was a scourge, and had been infecting humans around the world for millennia. Salk's vaccine was the first practical way to fight it, and it worked—polio was officially eliminated in the U.S. in 1979.

Salk's method was to kill various strains of the polio virus, then inject them into a patient. The patient's own immune system would then develop antibodies to the dead virus, preventing future infection by live viruses. Salk's first test subjects were patients who had already had polio ... and then himself and his family. His research was funded by grants, which prompted him to give away the vaccine after it was fully tested.

Clinical trials of Salk's vaccine began in 1954. By 1955 the trials proved it was both safe and effective, and mass vaccinations of American schoolchildren followed. The result was an immediate reduction in new cases. Salk became a celebrity because his vaccine saved so many lives so quickly.

Salk's vaccine required a shot. In 1962, Dr. Albert Sabin unveiled an oral vaccine using attenuated (weakened but not killed) polio virus. Sabin's vaccine was hard to test in America in the late 1950s, because so many people had been inoculated using the Salk vaccine. (Sabin did much of his testing in the Soviet Union.) Oral polio vaccine, whether with attenuated or dead virus, is still the preferred method of vaccination today. Polio isn't entirely eradicated around the world, though we're very close.

Here's a vintage newsreel from the mid 1950s telling the story:

For more information on Dr. Jonas Salk and his work, click here.

Drunken Thieves Tried Stealing Stones From Notre-Dame

Notre-Dame.
Notre-Dame.
Athanasio Gioumpasis, Getty Images

With Paris, France, joining a long list of locales shutting down due to coronavirus, two thieves decided the time was right to attempt a clumsy heist—stealing stones from the Notre-Dame cathedral.

The crime occurred last Tuesday, March 17, and appeared from the start to be ill-conceived. The two intruders entered the cathedral and were immediately spotted by guards, who phoned police. When authorities found them, the trespassers were apparently drunk and attempting to hide under a tarpaulin with a collection of stones they had taken from the premises. Both men were arrested.

It’s believed the offenders intended to sell the material for a profit. Stones from the property sometimes come up for sale on the black market, though most are fake.

The crime comes as Paris is not only dealing with the coronavirus pandemic but a massive effort to restore Notre-Dame after the cathedral was ravaged by a fire in 2019. That work has come to a halt in the wake of the health crisis, though would-be looters should take note that guards still patrol the property.

[h/t The Art Newspaper]

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