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 ...

This is a very different situation from the monohedral tilings that use regular hexagons. In those tilings, the repetitive structure is unavoidable. The geometry of the tiles themselves forces the ...

This week, mathematicians announced the discovery of a single tile shape that produces aperiodic patterns. It’s the latest advance in a field that stretches back decades.

The Penrose Tiling in the Bachelor Hall Courtyard presents acclaimed art and an international discovery for a mathematical puzzle unsolved for many years. Professors and students in math classes have ...

New 13 Sided and 14-Sided Shapes Can Tile Infinite Surfaces – Breakthrough in Math and Tiling June 10, 2023 by Brian Wang ADVERTISEMENT ...

A geometry problem that has been puzzling scientists for 60 years has likely just been solved by an amateur mathematician with a newly discovered 13-sided shape.

For mathematicians, the discovery appears to answer a long-standing question in the field of geometry. But for the rest of us, perhaps it represents a funky new option for bathroom tile.

The quest for the einstein tile—a shape never seen before in mathematics—turned up even more discoveries than mathematicians counted on ...

Self-affine tiles and fractal geometry form a rich field where geometric precision meets the complexity of nature’s form. At its core, the subject examines how self-affine tiles—constructed ...

geometry ‘Nasty’ Geometry Breaks Decades-Old Tiling Conjecture Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to ...