Often when describing patterns, they are placed in one of two categories: organic or geometric. Organic designs are ones ...

When most people think of shapes, they imagine a triangle, a rectangle, or maybe even a fancier-sounding rhombus or trapezoid. But to mathematicians, shapes encompass a vast universe of surprising ...

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 entire ...

A research team led by Maxim Kontsevich, a professor at the French Institute of Advanced Scientific Studies (IHES) and a 1998 Fields Medalist, has released a proof claiming to solve a long-standing pr ...

Researchers at Tsinghua University developed PriorFusion, a unified framework that integrates semantic, geometric, and ...