With a New, Improved ‘Einstein,’ Puzzlers Settle a Math Problem

A team of mathematical tilers made news in March by discovering an elusive “einstein”- a single shape that could tile a plane only in a non-repeating pattern. The researchers named their einstein “the hat.” However, Dr. Berger and others noted that the hat tiling used reflections – it included both the hat-shaped tile and its mirror image. So, David Smith, known as an “imaginative tinkerer,” got to work creating a monotile that does not use reflections, and two months later the team has one-upped itself with a new-and-improved einstein. The new monotile discovery advertises as “a weakly chiral aperiodic monotile” as it is aperiodic in a reflection-free universe but tiles periodically if allowed to use reflections. The team produced a family of strong or “strictly chiral aperiodic monotiles” named “Spectres,” owing to their curvy contours, only allow nonperiodic tilings, and without reflections. “A left-handed Spectre cannot interlock with its right-handed mirror image,” said Dr. Kaplan.

Author: OpenAI