For a long time, scientists associated crystal structures with an ordered arrangement of atoms in a repeating lattice-like pattern, believing it to be the most stable configuration. However, by the ...

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 ...

For some, tiles are rarely thought of unless it’s time for home renovations, but for mathematicians, they present plenty of conundrums—and a clever team has just cracked a particularly tricky one.

Consider the tiles on a bathroom floor or wall; they’re often arranged in a repeating pattern. But is there a single shape that tiles such a surface — an infinite one — in a pattern that never repeats ...

Dynamical systems and aperiodic order constitute a vibrant research area that bridges rigorous mathematical theory and applications across physics, materials science and engineering. By investigating ...

Gear-obsessed editors choose every product we review. We may earn commission if you buy from a link. Why Trust Us? The concept of aperiodic geometry has existed for at least 1,000 years from Islamic ...

Triangles and defects: Due to the chirality – the handedness – of the molecules, the individual triangular tiles never fit together perfectly. Defects and offsets occur, which give the surface its ...

The Sphere would not gravitationally bind to its star in a stable fashion. This is perhaps counterintuitive; you might think that a perfect sphere around a star would be stable. But if any part of the ...