Integral Tiling Pentagons

SummarySummaryFor four decades, Mathematics Magazine has chronicled the quest to find all convex pentagons that tile the plane. Illustrating this story physically leads to the question: What integer-sided convex pentagons tile the plane? Using results from classical number theory along with convexity and continuity principles, we provide a complete answer to this question.MSC:: Primary 52C20Secondary 11D09 AcknowledgmentsAlissa S. Crans is grateful to the Simons Foundation for their support of this work (#360097, Alissa Crans).Additional informationFundingAlissa S. Crans is grateful to the Simons Foundation for their support of this work (#360097, Alissa Crans).Notes on contributorsAlissa S. CransAlissa S. Crans (MR Author ID: 676843) has been recognized nationally for her enthusiastic ability to share and communicate mathematics. A professor of mathematics at Loyola Marymount University, Alissa is known for her active mentoring and supporting of women, underrepresented students, and junior faculty. Outside of mathematics, you can find her rehearsing with the Santa Monica College Wind Ensemble, running along the Venice Beach boardwalk, or on her quest to find the spiciest salsa on the Westside.Glen T. WhitneyGlen T. Whitney (MR Author ID: 305737) trained as a logician, became a quantitative analyst at a hedge fund, and then founded the National Museum of Mathematics. From teaching at Harvard and Rutgers to leading public constructions such as a 20 foot tall Sierpinski tetrahedron, Glen continues to promote the importance of illustrating mathematics. He has a serial habit of editing problems columns: “Varsity Math” in the Wall Street Journal, “The Playground” in Math Horizons, and currently the “Prisoner’s Dilemma” for the Prison Math Project.