Tiling the Plane with Congruent Pentagons

Abstract

The importance of recreational mathematics and the involvement of amateur mathematicians has been dramatically demonstrated recently in connection with the prob/ lem of tiling the plane with congruent pentagons. The problem is to describe completely all 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], [191. 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 of pentagons and each discovered pentagons missing from Kershner's list. New interest in the problem has been aroused and both amateur and professional mathematicians are presently working on its solution.