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Monday, December 1, 2014

Math, Women, Tessellation, Intuition

(image: WikimediaCommons)

A lot of discussion around the Web these days about women in STEM, and at Math-Frolic I'm even more interested in women in math, so thought it would be fun/timely to recount the unusual story of Marjorie Rice -- worth repeating, even if most are familiar with it, as a rare instance of someone becoming involved with math almost by accident.
[Most of this information was reported over a year ago in a MathMunch piece on Marjorie here:
http://mathmunch.org/2013/02/25/marjorie-rice-inspired-by-math-and-subways/  also see Ivars Peterson's 2010 piece here: http://mathtourist.blogspot.com/2010/06/tiling-with-pentagons.html ]

Marjorie discovered her senior year in high school that she found math interesting, but by then it was too late to do much with it. She went on to marry, have children, be a housewife; i.e. she took NO mathematics past high school. But after getting a subscription to Scientific American for her son, she began reading the Mathematical Games column of Martin Gardner, including a 1975 column concerning "pentagon tessellations," i.e. pentagon forms that could cover an entire plane, repeating themselves with no gaps, like a jigsaw puzzle. At one time mathematicians believed there were only five such pentagon shapes that achieved tessellation, but in 1968 three more were discovered, and a fourth new one had just been added in 1975 that Gardner was reporting on.

Marjorie was intrigued. And playing with different pentagons, with different internal angles, she finally found a fresh one that accomplished the feat of tessellation. Inventing her own unconventional notation to describe her work she wrote to Gardner showing the result. And he sent her correspondence on to another female mathematician, Doris Schattschneider, who confirmed Marjorie's success and translated her work into more standard mathematical format.  Marjorie went on to find yet three more successful pentagon tessellations, and also DISproved a conjecture made by Doris.
Successful amateurs have made significant contributions to astronomy, but in most sciences, and particularly in mathematics, it is rare for an academically-untrained amateur to accomplish something missed by professionals... but apparently Marjorie didn't know that! Her own website on her work is here:

She is now over ninety, and remains an inspiration, not just to women, but to amateur enthusiasts everywhere. What I love most though about the Marjorie Rice story isn't that she was a female in mathematics, nor even that she was an amateur contributing to a technical field, but rather what the story says about the role of intuition and insight in math. Despite mathematics' image of being cold, dry, and rigid, and despite its abstractness in advanced study, scrape below the surface and there remains, on occasion, a powerful substrate of intuition and mental imagery, accessible to many.

Below is a video segment (from about the 31:50 point to 35:45) talking about Marjorie's work (again h/t to MathMunch for this):

We now know of 14 tessellating pentagon forms! Are there more?

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