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 ...

Look carefully! Mathematicians have invented a new 13-sided shape that can be tiled infinitely without ever repeating a pattern. They call it "the einstein." For decades, mathematicians wondered if it ...

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 ...

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 ...

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 ...

New research sheds light on how a certain kind of pattern in nature arises. Nature is full of patterns. Among them are tiling patterns, which mimic what you'd see on a tiled bathroom floor, ...