WASHINGTON – Those wondrously intricate tile mosaics that adorn medieval Islamic architecture may cloak a mastery of geometry not matched in the West for hundreds of years. Historians have long ...

One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

Remember the graph paper you used at school, the kind that’s covered with tiny squares? It’s the perfect illustration of what mathematicians call a “periodic tiling of space”, with shapes covering an ...

Patterning and periodic structures are very important in physics. This led to a tremendous amount of work on learning what shapes can tile an area or fill a volume. It was found that these shapes must ...

The recently discovered “hat” aperiodic monotile admits tilings of the plane, but none that are periodic [SMKGS23]. This polygon settles the question of whether a single shape—a closed topological ...

BOTHELL — One person’s idle doodling is another’s mathematical breakthrough. Two mathematics professors and one of their former students at the University of Washington at Bothell have made a ...

Henry Adams does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

The first such non-repeating, or aperiodic, pattern relied on a set of 20,426 different tiles. Mathematicians wanted to know if they could drive that number down. By the mid-1970s, Roger Penrose (who ...