About Marjorie Rice

Any triangle can tile the plane. Any quadrilateral can tile the plane — even non-convex ones. Some hexagons can tile the plane but no polygons of seven or more sides. There are exactly fifteen types of pentagons that tile the plane, four of which were discovered by amateur mathematician Marjorie Rice between 1975 and 1977.

Responding to a column by Martin Gardner in the July 1975 issue of Scientific American, titled “On tessellating the plane with convex polygon tiles”, Rice set out to find new types of pentagonal tilings in addition to the eight types of tilings that were previously discovered by other mathematicians. 

Living in San Diego, Marjorie Rice was at the time a fifty two year old home maker and a mother of five children. She worked in secret at her kitchen table on the tessellation problem — none of her family was aware. Without any background in mathematics, she devised a new symbolic notation system to classify the known tilings and started her search for new ones.   

Within a few months, in February 1976, she shared a new tiling (type 9) with Martin Gardner:

Dear Mr. Gardner, ... Here is a pentagonal tile that I believe really is different from any you have listed though similar to types 7 an 8 ... Sincerely, Marjorie Rice

Gardner passed this on to Doris Schattschneider, an American mathematician specialised in tiling patterns, to verify this was actually a new tessellation. Schattschneider was able to validate Rice’s discovery. Over the years, and in continuous correspondence with Doris Schattschneider, Rice discovered three more types of pentagons that tile the plane. Her work was published in Mathematics Magazine by Schattschneider in 1977. In 1999 her last discovery, the type 13 tiling, was installed  on the floor of the foyer of the Mathematical Association of America.