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Pentagon tessellation7/3/2023 Other amateurs have also made major tiling discoveries. … When I look in her files, I see octagons and hexagons.” Kathy Rice said: “My mom continued investigating. She commemorated her pentagon patterns in Escher-esque paintings. She was interviewed for “The Nature of Things” documentary in 1996, and a tile floor in the lobby of the Mathematical Association of America in Washington exhibits one of her pentagon tessellations. Rice still said nothing of her achievements to her children, but they eventually found out as the accolades mounted. Rice declined to lecture on her discoveries, citing shyness, but at Schattschneider’s invitation, she and her husband attended a university mathematics meeting, where she was introduced to the audience. “These considerations forced conditions on the angles and sides of the pentagon if it was to tile,” Schattschneider explained in a journal article, “thus giving either a description of a pentagon which could tile in a prescribed manner, or forcing the conclusion that no pentagon could be constructed which satisfied the conditions.” Using this method, Rice eventually found four new tessellating convex pentagons and nearly 60 different tessellations. Rice’s approach - the same one taken by Michaël Rao in his new computer-assisted proof - had been to consider the different ways that the corners of a pentagon could possibly come together at vertices of a tiling. Schattschneider confirmed that Rice’s finding was correct. “He would never have spent hours finding patterns when he thought there were other things that needed our attention.” “My dad had no idea what my mom was doing and discovering,” Kathy said. Lacking a mathematical background, I developed my own notation system and in a few months discovered a new type.”Īstonished and delighted, she sent her work to Gardner, who sent it to Doris Schattschneider, a tiling expert at Moravian College in Pennsylvania. When she read Gardner’s column about tiling, as she later recalled in an interview on David Suzuki’s “The Nature of Things”: “I thought, my, that must be wonderful that someone could discover these things which no one had seen before, these beautiful patterns.” She also wrote in an essay, “I became fascinated by the subject and wanted to understand what made each type unique. Rice gave one of her sons a subscription to Scientific American partly so she could peruse it while the children were at school. “She was fascinated with the golden ratio” and pyramids, he wrote, and studied them “with extensive drawings and calculations.” “We were kind of raised with the importance of the Scriptures and studying that way,” Kathy said, “and you didn’t want to waste your time on other endeavors.” Still, Rice read avidly and used her mind “actively, deeply and regularly,” as her son David wrote in an obituary shared among friends and family. That child died but five other children survived.įor Rice, math was an indulgence. Marjorie Rice worked for a time as a commercial artist, until the couple moved to San Diego with their infant son. In 1945, she married Gilbert Rice, a deeply Christian conscientious objector, and they moved to Washington, D.C., where Gilbert was to work in a military hospital. Though she loved learning and particularly her brief exposure to math, poverty and cultural norms prevented her family from even considering that she might attend college. As I report in Quanta today, a new computer-assisted proof by the French mathematician Michaël Rao establishes that there are precisely 15 families of convex pentagons that tile the plane - including the four that Rice discovered.īorn Marjorie Jeuck in Florida, Rice went to a one-room country school where she skipped two grades and studied with the older kids. Dementia prevented her from learning that the pentagon tiling story has finally come to a close, decades after Gardner first called it. "6-fold pentille tiling".Rice died on July 2 at the age of 94. One angle measures 60°, the other four measure 120°. If the short edge has length 1, the long edges have length 2. Įach face of this tiling is an irregular pentagon with 3 short and 2 long edges. In the classification of isohedral tilings of the planes with convex pentagonal faces, it is type 5 of 15. It is the dual of the uniform snub trihexagonal tiling. The floret pentagonal tiling, also called the order-6 pentille tiling, is an isohedral tiling with floret pentagons for faces, joining 3 or 6 to a vertex.
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