Marjorie Rice (1923-2017) is an unlikely mathematician. She never got further than a year of high school math education. And yet, she discovered geometric patterns that had never been found before.
Marjorie Rice (1923-2017) is an unlikely mathematician. She never got further than a year of high school math education. And yet, she discovered geometric patterns that had never been found before.
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Hello, from Wonder Media Network, I’m Jenny Kaplan and this is Womanica.
This month, we're highlighting women who've led dynamic lives. Ones that have shifted, evolved and bloomed, often later in life.
Our story today features an unlikely mathematician. She never got further than a year of high school math education. And yet, she discovered geometric patterns that had never been found before. Let’s talk about the surprising Marjorie Rice.
Marjorie was born in 1923 in Florida. Shortly after, her family moved to a farm in Southern Oregon. There, she attended a one-room country school where she quickly showed an aptitude for math. Marjorie later wrote, “Arithmetic was easy and I liked to discover the reasons behind the methods we used.”
As a teen, Marjorie’s family moved back to Florida. She enrolled in the local high school where she followed a more traditional, secretarial track. She took the required general math course But beyond that, she didn’t pursue mathematics or science.
Marjorie went on to work a handful of jobs, before getting married in 1945, at the age of 22. She and her new husband, Gilbert moved to San Diego and started a large family.
Gilbert and Marjorie raised their family with traditional christian values and gender roles. Marjorie took on the role of homemaker, and focused on raising the children.
When her eldest son was in junior high, she assisted with his math homework. She also learned a new style of math alongside him. Marjorie later wrote, “I could often find solutions to his problems by unorthodox means, since I did not know the correct procedures. I enjoyed puzzles of all kinds.”
Marjorie’s life changed course when she got her youngest son a subscription to Scientific American. While the magazine was technically a gift, Marjorie allowed herself the indulgence of reading it while her children were at school. She was particularly interested in the “Mathematical Games” column written by Martin Gardner. In December of 1975, the column sent Marjorie down an unexpected path.
The column revolved around a math concept called ‘tiling the plane,’ also known as tessellation. For non-mathematicians, this phenomenon occurs when a shape can repeat and cover a flat surface without gaps or overlapping. If you think of square tiles, that obviously works. But circles? That would leave gaps. Martin Gardner and other mathematicians were interested in how that rule applied to shapes with more sides – like pentagons. At the time, mathematicians believed that only eight types of convex pentagons could tile the plane. That is, until a Scientific American reader found another type of pentagon that worked. This led Martin Gardner to suggest perhaps additional types existed.
Marjorie was hooked. She set out to find her own examples of tiling pentagons.
In an interview Marjorie recalled “I thought, my, that must be wonderful that someone could discover these things which no one had seen before, these beautiful patterns.”
She didn’t have any formal training in geometry. So, Marjorie developed her own notation systems to organize the known types of tiling pentagons. She worked in secret while home alone.
Just two months later, in February of 1976, Marjorie discovered a new type of tessellating pentagon. Giddy, she sent her findings to Martin Gardner himself. He passed them along to a tiling expert, Doris Schattschneider at Moravian College in Pennsylvania. Doris verified that Marjorie’s discovery was indeed accurate and began corresponding with her directly.Doris sent Marjorie articles about tiling which spurred further research. In December of that same year, Marjorie discovered two additional types of tiling pentagons. A year later, she discovered another. Marjorie had found four new pentagon patterns in total.
All the while, Marjorie didn’t reveal her mathematical breakthroughs to her family, or anyone else really. It is largely thanks to Doris that we know about contributions to mathematics today.
It wasn’t until the accolades started mounting that her children found out about their mother’s unique hobby. In the 1990s, she was interviewed for the documentary, “The Nature of Things.” And one of her patterns was even transformed into ceramic tiles for the foyer of the Mathematical Association of America Headquarters in Washington D.C.
Marjorie never lectured on her discoveries, always insisting she was far too shy. However, at one of Doris’ lectures to the Mathematical Association of America, she introduced Marjorie. Marjorie stood. And in response, the audience rose to their feet and gave her a standing ovation.
Marjorie lived with dementia for the last decade of her life. This meant she didn’t learn about the end of this pentagon tiling story. In 2017, another scientist, with help from a computer program, determined that all of the possible tessellating pentagons had been discovered. Four out of the total fifteen were Marjorie’s.
Marjorie died that same year, in 2017. She never stopped exploring these math puzzles. Her daughter said Marjorie always did it, “just for the sake of discovery.”
All month, we’re highlighting dynamos. For more information, find us on Facebook and Instagram @womanicapodcast.
Special thanks to Liz Kaplan, my favorite sister and co-creator.
Talk to you tomorrow!