Editors' Note: Doris Schattschneider received her PhD from Yale University in 1966. She has written extensively on polyhedra, tiling, symmetry, and the connections between geometry and art, especially the work of M. C. Escher. Her books on Escher are M.C. Escher Kaleidocycles, with WallaceWalker (Pomegranate, 1987), M. C. Escher's Legacy: A Centennial Celebration, with Michele Emmer, (Springer, 2003), and M. C. Escher: Visions of Symmetry (new edition, Harry Abrams, 2004).

From 1981 to 1985 Professor Schattschneider served as editor of Mathematics Magazine. In 1993 she received the MAA's Award for Distinguished College or University Teaching of Mathematics. For the article we see here she was awarded the MAA's Allendoerfer Award in 1979.

She is Professor Emerita of Mathematics at Moravian College, where she joined the faculty in 1968 after appointments at Northwestern University and the University of Illinois, Chicago.

The importance of recreational mathematics and the involvement of amateur mathematicians has been dramatically demonstrated recently in connection with the problem of tiling the plane with congruent pentagons. The problem is to describe completely all convex pentagons whose congruent images will tile the plane (without overlaps or gaps). The problem was thought to have been solved by R. B. Kershner, who announced his results in 1968 [18], [19]. In July, 1975, Kershner's article was the main topic of Martin Gardner's column, “Mathematical Games” in Scientific American. Inspired by the challenge of the problem, at least two readers attempted their own tilings with pentagons and each discovered pentagons missing from Kershner's list.