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A Brief History of Tricky Mathematical Tiling
The discovery earlier this year of the “hat” tile marked the culmination of hundreds of years of work into tiles and their symmetries.
Math Patterns That Go On Forever but Never Repeat
Simple math can help explain the complexities of the newly discovered aperiodic monotile.
Hobbyist Finds Math’s Elusive ‘Einstein’ 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.
‘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 emerge. But they were wrong.
Undergraduates Hunt for Special Tetrahedra That Fit Together
A group of MIT undergraduates is searching for tetrahedra that tile space, the latest effort in a millennia-long inquiry. They’ve already made a new discovery.
Computer Search Settles 90-Year-Old Math Problem
By translating Keller’s conjecture into a computer-friendly search for a type of graph, researchers have finally resolved a problem about covering spaces with tiles.
The (Math) Problem With Pentagons
Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?
Marjorie Rice’s Secret Pentagons
A California housewife who in the 1970s discovered four new types of tessellating pentagons is dead at 94.
Pentagon Tiling Proof Solves Century-Old Math Problem
A French mathematician has completed the classification of all convex pentagons, and therefore all convex polygons, that tile the plane.