After a decade of attempts, David Smith, a shape hobbyist, has discovered an "einstein," an aperiodic monotile that tiles a plane in a nonrepeating pattern. Smith's einstein, called "the hat," is a polykite made of eight kites. The paper, co-authored by Smith and three others, provides two proofs of the hat's aperiodicity, one of which uses a new technique. The hat's discovery opens up new possibilities for materials with this type of internal structure.
After a decade of attempts, a self-described shape hobbyist from England, David Smith, has discovered an "einstein," an aperiodic monotile that tiles a plane in a nonrepeating pattern. Smith's discovery, called "the hat," was confirmed in a new paper by Smith and three co-authors with mathematical and computational expertise. The paper provides two proofs, one of which offers a new tool for proving aperiodicity. The hat is a polykite made of eight kites and is part of an entire family of related einsteins, including a second one discovered by Smith called "the turtle."
