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 ...

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 ...

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. Subscribe to read this story ad-free ...

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 ...