Consider the tiles on a bathroom floor or wall; they’re often arranged in a repeating pattern. But is there a single shape that tiles such a surface — an infinite one — in a pattern that never repeats ...

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 surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way. In mid-November of ...

When Peter J. Lu traveled to Uzbekistan, he had no idea of the mathematical journey that he was about to embark on as well. The Harvard graduate student in physics was fascinated by the beautiful and ...

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 ...