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 ...

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 ...

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 ...

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 ...

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 story behind the installation of these gorgeous mathematically shaped tiles was remarkable and accounted for by articles of the main persons behind the idea, math professor emeritus Prof. Milton ...

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 ...