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

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 ...

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 ...

A 13-sided shape known as “the hat” has mathematicians tipping their caps. It’s the first true example of an “einstein,” a single shape that forms a special tiling of a plane: Like bathroom floor tile ...

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 ...

Mathematicians show “soft cell” shapes are abundant in natural world. Soft cells are described as natural tiles with curved edges—a stark contrast to the mathematical solutions for creating tiling ...

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 ...