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 ...
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 ...
Have you ever admired how the slats of a hardwood floor fit together so cleanly, or how the hexagons underneath your bathroom rug perfectly meet up? These are examples of geometric tilings, ...
The swirling Arabesque ceramic tiles used in medieval Islamic mosaics and architecture were produced using geometry not understood in the West until the 1970s, a new study suggests. The inlaid ...
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 ...
Creatively tiling a bathroom floor isn’t just a stressful task for DIY home renovators. It is also one of the hardest problems in mathematics. For centuries, experts have been studying the special ...
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