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 ...

Infinitely many copies of a 13-sided shape can be arranged with no overlaps or gaps in a pattern that never repeats. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY ...

The same researchers behind the 13-sided "hat" shape have stumbled upon a version that improves upon the original in a very important way. Reading time 2 minutes In March, a group of mathematicians ...

Mathematicians have discovered a single shape that can be used to cover a surface completely without ever creating a repeating pattern. The long-sought shape is surprisingly simple but has taken ...

It’s been just months since researchers reported the first “einstein” — a single tile that can cover an infinite plane, but only with a pattern that never repeats (SN: 3/24/23). Now, the same team has ...

Mathematicians solved a decades-long mystery earlier this year when they discovered a shape that can cover a surface completely without ever creating a repeating pattern. But the breakthrough had come ...

Simple patterns can be found almost everywhere in the environment, from drain covers to leaves and road markings, say Julie Mountain and Felicity Robinson Patterns are essential to building ...