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Marjorie Rice

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Tiling a plane means covering a flat surface with shapes. These shapes must fit together perfectly without any gaps or overlaps. This process is also called tessellation. While shapes like squares tile easily, certain other shapes are much harder to use. Marjorie Ruth Rice was an American amateur mathematician who focused on a difficult problem. She studied how convex pentagons, or five-sided shapes, can tile a plane.

PentagonTilings Rice 2x2
PentagonTilings Rice 2x2

Rice was a mother of five living in San Diego, California. She did not have a professional degree in mathematics. Instead, she had a high-school education and some training in commercial art. She became fascinated by math through a magazine column. The column was called "Mathematical Games" by Martin Gardner in Scientific American. Rice would often rush to get the magazine from the mail. She read a 1975 article about how convex polygons tile a plane. That article suggested the list of pentagon tilers was already complete.

Prototile p5-type9
Prototile p5-type9

However, the completeness of the list was soon challenged. A reader named Richard James III found a new pentagon tiler. Gardner published this discovery in December 1975. This news inspired Rice to start her own investigations. She worked on these problems during her free time. She often drew diagrams on her kitchen table. She would hide her work when her husband or children returned. She even developed her own unique system of notation. This system used special marks to show the relationships between sides and angles.

P5-type11 chiral coloring
P5-type11 chiral coloring

Rice's discoveries happened in rapid stages. In February 1976, she found a new pentagon type and its variations. She sent these results to Gardner using her homemade notation. Gardner sent her work to Doris Schattschneider, a tiling expert. Schattschneider was initially skeptical of the strange symbols. She described the notation as looking like "hieroglyphics." After careful study, Schattschneider validated that Rice's results were correct.

P5-type12-chiral coloring
P5-type12-chiral coloring

By October 1976, Rice had found 58 different pentagon tilings. Most of these were previously unknown to mathematicians. She organized these into 12 distinct classes. These tilings were "2-block transitive," meaning two pentagons must be joined to tile the plane. By December 1976, she found two more new types. These created over 75 distinct tessellations in blocks that looked like double hexagons. By December 1977, she discovered her fourth new type of tile. By that time, she had identified 103 of these 2-block transitive tilings.

P5-type13-chiral coloring
P5-type13-chiral coloring

Rice's achievements earned her significant respect in the math community. In 1995, Doris Schattschneider gave a lecture about Rice's work in Los Angeles. At the end of the talk, the audience gave Rice a standing ovation. Her patterns even became part of a physical building. In 1999, one of her tilings was used for the floor in the Mathematical Association of America headquarters. This building is located in Washington, D.C. Her work proved that amateur researchers can make major scientific contributions.

Marjorie Rice was born in St. Petersburg, Florida, in 1923. She died in San Diego in 2017. Her mathematical papers are preserved today in Canada. They are held at the University of Calgary Library in the Eugène Strens Recreational Mathematics Collection. Her life is also celebrated in literature. A children's book titled "The Five Sides of Marjorie Rice" was published in 2025. Her story connects the world of art and the world of geometry. It shows how curiosity can lead to new mathematical truths.

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🖼️ Images & Media (9)
File:PentagonTilings Rice 2x2.svg
PentagonTilings Rice 2x2.svg
File:P5-type9-chiral_coloring.png
P5-type9-chiral_coloring.png
File:P5-type11 chiral_coloring.png
P5-type11 chiral_coloring.png
File:P5-type12-chiral_coloring.png
P5-type12-chiral_coloring.png
File:P5-type13-chiral_coloring.png
P5-type13-chiral_coloring.png
File:Prototile p5-type9.png
Prototile p5-type9.png
File:Prototile p5-type11.png
Prototile p5-type11.png
File:Prototile p5-type12.png
Prototile p5-type12.png
File:Prototile p5-type13.png
Prototile p5-type13.png
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