Marjorie Rice

Rice was born February 16, 1923, in St. Petersburg, Florida.

File:PentagonTilings Rice 2x2.svg

Marjorie Rice was a San Diego{{cite web |last1=Mulcahy |first1=Colm |author1-link=Colm Mulcahy |title=Martin Gardner at 101 ("It's as not-so-easy as 3, 4, 5") |url=https://blogs.scientificamerican.com/guest-blog/martin-gardner-at-101-it-s-as-not-so-easy-as-3-4-5/ |website=Scientific American Blog Network |access-date=14 December 2021 |language=en |date=October 28, 2015}} mother of five, who had become an ardent follower of Martin Gardner's long-running column, "Mathematical Games", which appeared monthly, 1957–1986, in the pages of Scientific American magazine. By the 1970s, Gardner was a popular science writer and amateur mathematician. Rice said later that she would rush to grab each issue from the mail before anyone else could get it, especially her son who subscribed to the magazine.{{cite news|last=Cole|first=K. C.|title=Beating the Pros to the Punch|date=March 11, 1998|url=https://www.latimes.com/archives/la-xpm-1998-mar-11-mn-27706-story.html |newspaper=Los Angeles Times |page=1 |id={{ProQuest|421258615}} |archive-url=https://web.archive.org/web/20151106221324/http://articles.latimes.com/1998/mar/11/news/mn-27706 |archive-date=November 6, 2015 |url-status=live }}

In 1975, Rice read Gardner's July column, "On Tessellating the Plane with Convex Polygon Tiles", that discussed what kinds of convex polygons can fit together perfectly without any overlaps or gaps to fill the plane. In his column, Gardner indicated that "the task of finding all convex polygons that tile the plane …. was not completed until 1967 when Richard Brandon Kershner … found three pentagonal tilers that had been missed by all predecessors who had worked on the problem".{{cite magazine|last=Gardner |first=Martin |title=On tessellating the plane with convex polygon tiles |department=Mathematical Games |magazine=Scientific American |date=July 1975 |pages=112–117 |jstor=24949848}} Gardner was repeating Kershner's claim that the list of convex pentagon tilers was complete. But within a month, Gardner received an example, by one of his readers, Richard James III,{{cite web |last1=Britton |first1=Jill |author1-link=Jill Britton |title=Perplexing Pentagons |url=https://britton.disted.camosun.bc.ca/jbperplex.htm |website=Distributed Education |publisher=Camosun College |access-date=14 December 2021 |archive-url=https://web.archive.org/web/20060109162507/https://britton.disted.camosun.bc.ca/jbperplex.htm |archive-date=9 January 2006}} of a new convex pentagon tiler, and published this news in his December 1975 column.{{cite magazine|last=Gardner |first=Martin |title=A random assortment of puzzles, together with reader responses to earlier problems |department=Mathematical Games |magazine=Scientific American |date=December 1975 |pages=116–119 |jstor=24949967}}

Inspired by this new discovery, Rice decided to try to find other new pentagon tilers. Despite having only a high-school education, but a keen interest in art, she began devoting her free time to discovering new pentagonal tilings, ways to tile a plane using pentagons. She worked on the problem in her free time and through the 1975 holiday season "by drawing diagrams on the kitchen table when no one was around and hiding them when her husband and children came home, or when friends stopped by". She even developed her own system of notation to represent the constraints on and relationships between the sides and angles of the pentagons.

By February 1976, she had discovered a new pentagon type and its variations in shape and drew up several tessellations by these pentagon tiles. She mailed her discoveries to Gardner using her own home-made notation. He, in turn, sent Rice's work to Doris Schattschneider, an expert in tiling patterns, who was skeptical at first, saying that Rice's idiosyncratic notation system seemed odd, like "hieroglyphics". But with careful examination, she was able to validate Rice's results.

By October 1976, Rice had discovered 58 pentagon tilings that needed two pentagons stuck together in order to tile "transitively" (most of them previously unknown), which she arranged into 12 classes.{{cite web |author1-link=Ed Pegg Jr.|last1=Pegg |first1=Ed Jr. |title=The 14 Different Types of Convex Pentagons that Tile the Plane |url=https://www.mathpuzzle.com/tilepent.html |website=mathpuzzle |access-date=14 December 2021}} By December 1976, she had discovered two additional new types of tessellating pentagons and over 75 distinct tessellations by pentagons that were in blocks that could be seen as "double hexagons". In December 1977, she made her fourth discovery of a new type of pentagon tiler and by then had enumerated 103 "2-block transitive" pentagon tilings.{{cite journal |last1=Schattschneider |first1=Doris |title=Marjorie Rice and the MAA tiling |journal=Journal of Mathematics and the Arts |date=2018 |volume=12 |issue=2–3 |pages=114–127 |doi=10.1080/17513472.2018.1453740|s2cid=125461075 }}

Rice had a keen interest in art, and had completed half of a correspondence course in commercial art before she married. Throughout her investigations, she explored how to use pentagonal tilings as grids on which to overlay tessellations of flowers, shells, butterflies and bees.

Rice's discoveries were never published in Gardner's Scientific American columns, but were revealed in an addendum to his original column that was included in his 1988 collection of columns, where he declared her discoveries "fantastic achievements".{{cite book|last=Gardner |first= Martin |chapter=Tiling with Convex Polygons |title=Time Travel and Other Mathematical Bewilderments |publisher=W.H. Freeman |location=New York |date=1988 |pages=163–176 |isbn=0-7167-1924-X}}

"Much of Rice’s investigations remain unpublished, in that only the product of her investigations are shown. How she devised these is not generally shown. However, some of her investigations are indeed shown in The Mathematical Gardner, a compilation of articles in honour of the late Martin Gardner, with Doris Schattschneider’s article In Praise of Amateurs (mostly concerning background detail on Rice’s pentagon tiling findings), pages 140-166. Pages 154-155 contain numerous convex pentagon tilings".{{cite book|first=Doris |last=Schattschneider |chapter=In Praise of Amateurs |editor-first=David A. |editor-last=Klarner |title=The Mathematical Gardner |pages=140–166 |publisher=Prindle, Weber & Schmidt |location=Boston |date=1981 |doi=10.1007/978-1-4684-6686-7_16 |isbn=978-1-4684-6688-1 |url= http://www.math.jhu.edu/~eriehl/301/Schattschneider-Amateurs.pdf}} Reprinted as Mathematical Recreations: A Collection in Honor of Martin Gardner, Mineloa, NY: Dover, 1998{{cite web |last1=Bailey |first1=David |title=Pentagon Tilings |url=http://www.tess-elation.co.uk/pentagon-tilings |website=World of Tessellations |access-date=14 December 2021}}

Rice's archival fonds are at the University of Calgary Library, Alberta, Canada, in the ''Eugène Strens

• {{cite web |title=Strens, Eugène |url=https://searcharchives.ucalgary.ca/strens-eugene |website=Archives |publisher=searcharchives.ucalgary.ca |access-date=16 December 2021}}
• {{cite book |last1=Guy |first1=Richard K. |last2=Woodrow |first2=Robert E. |title=The Lighter Side of Mathematics: Proceedings of the Eugene Strens Memorial Conference on Recreational Mathematics and Its History |date=3 August 2020 |publisher=American Mathematical Society |isbn=978-1-4704-5731-0 |page=7 |url=https://books.google.com/books?id=FsH2DwAAQBAJ&dq=Eug%C3%A8ne+Strens&pg=PA7 |language=en}}
• {{cite web |title=Eugène Strens (1899-1980) |url=https://data.bnf.fr/fr/14559814/eugene_strens/ |website=data.bnf.fr |access-date=16 December 2021 |language=fr}}

Recreational Mathematics Collection''.{{cite web |title=Marjorie Rice fonds |url=https://searcharchives.ucalgary.ca/marjorie-rice-fonds |website=Archives |publisher=University of Calgary |access-date=16 December 2021}}

In 1995, at a regional meeting of the Mathematical Association of America held in Los Angeles, Schattschneider convinced Rice and her husband to attend her lecture on Rice's work. Before concluding her talk, Schattschneider introduced Rice. "And everybody in the room . . . gave her a standing ovation."

In 1999, one of Rice's tilings became the basis for the floor in the foyer of the headquarters of the Mathematical Association of America in Washington, D.C.

Rice's papers and materials in support of her mathematical discoveries are preserved at the Eugène Strens Recreational Mathematics Collection at the University of Calgary Library, Alberta, Canada.{{cite journal |last1=Schattschneider |first1=Doris |title=Marjorie Rice (16 February 1923–2 July 2017) |journal=Journal of Mathematics and the Arts |date=2017 |volume=12 |issue=1 |pages=51–54 |doi=10.1080/17513472.2017.1399680|doi-access=free}}

Marjorie Ruth Jeuck married Gilbert Rice in 1945.{{cite web |title=San Jose Mercury News |url=https://searcharchives.ucalgary.ca/san-jose-mercury-news |website=Archives |publisher=searcharchives.ucalgary.ca |access-date=16 December 2021 |quote=File consists of news clipping of article featuring Rice from February 28, 1995 issue of San Jose Mercury News. Includes quotes from Marjorie and her husband, Gilbert, as well as quotes from Doris Schattschneider's lecture at San Francisco mathematics conference.}}{{Cite web |last=Wolchover |first=Natalie |date=2017-07-11 |title=Marjorie Rice's Secret Pentagons |url=https://www.quantamagazine.org/marjorie-rices-secret-pentagons-20170711/ |access-date=2022-07-26 |website=Quanta Magazine |language=en}} She had six children, of whom one did not live past infancy.

Rice died July 2, 2017, in San Diego, California.

{{Reflist}}

• {{cite book|last=Rice |first=Marjorie |chapter=Escher-Like Patterns from Pentagonal Tilings |editor1-last=Schattschneider |editor1-first=Doris |editor2-last=Emmer |editor2-first=Michele |title=M.C. Escher's Legacy: A Centennial Celebration |year=2003 |publisher=Springer |location=Berlin |doi=10.1007/3-540-28849-X_24 |pages=244–251 |isbn=978-3-540-20100-7 |ref=none}}
• {{cite journal |last1=Schattschneider |first1=Doris |title=Tiling the Plane with Congruent Pentagons |journal=Mathematics Magazine |date=1978 |volume=51 |issue=1 |pages=29–44 |doi=10.1080/0025570X.1978.11976672 |jstor=2689644 |url=https://www.maa.org/sites/default/files/images/upload_library/22/Allendoerfer/1979/0025570x.di021103.02p0247f.pdf |ref=none}} Reprinted with Afterword in The Harmony of the World: 75 Years of Mathematics Magazine, eds. Gerald Alexanderson and Peter Ross, Mathematical Association of America, 2007, pp. 175–190
• {{cite journal |last1=Schattschneider |first1=Doris |title=Errata |department=News & Letters |journal=Mathematics Magazine |date=1978 |volume=51 |issue=4 |page=256 |doi=10.1080/0025570X.1978.11976726 |jstor=2689477 |ref=none}}
• {{cite book |chapter-url= http://archive.bridgesmathart.org/2018/bridges2018-1.pdf|chapter=Marjorie Rice and Her Pentagonal Tilings |last1=Schattschneider |first1=Doris |date=2018 |isbn=978-1-938664-27-4 |title=Bridges Stockholm 2018 |publisher=Tessellations Publishing |location=Phoenix |pages=1–2 |ref=none}}

• Marjorie Rice [https://sites.google.com/site/intriguingtessellations/home Intriguing Tessellations] (home page) {{webarchive |url=https://web.archive.org/web/20070820095233/http://tessellations.home.comcast.net/|date=August 20, 2007}}
• [http://demonstrations.wolfram.com/PentagonTilings/ Pentagon Tilings demonstration] - Wolfram Research
• {{cite web |last1=Schattschneider |first1=Doris |author1-link=Doris Schattschneider |title=The Story of Marjorie Rice |url=https://www.youtube.com/watch?v=q2gs9LpICCk |website=Gathering 4 Gardner Celebration of Mind |language=en |via=YouTube}}
• {{cite web |last1=Sellaroli |first1=Giuseppe |last2=Garcia |first2=Amanda |title=A brief history of: pentagonal tilings (1918-2018)) |url=https://sequentialmath.com/comic/a-brief-history-of-pentagonal-tilings |website=Sequential Math |date=June 1, 2018 |quote=cartoon with references}}

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Category:1923 births

Category:2017 deaths

Category:20th-century American mathematicians

Category:20th-century American women mathematicians

Category:21st-century American mathematicians

Category:21st-century American women mathematicians

Category:Amateur mathematicians

Category:American geometers

Category:Mathematicians from Florida

Category:People from St. Petersburg, Florida