Explaining the complex structure of tropical forests is one of the great challenges in ecology. An issue of special interest is the distribution of different sizes of trees, something which is of ...

In a pair of papers posted online this month, a Ukrainian mathematician has solved two high-dimensional versions of the centuries-old “sphere packing” problem. In dimensions eight and 24 (the latter ...

Sphere packing and crystallization involve the study of how identical particles arrange themselves in space under pairwise interactions, with sphere packing focusing on the densest arrangement of ...

Have you ever wondered about the best way to pack a finite number of identical spheres into a shape-shifting flexible container, like a convex hull? An intuitively simple problem concerning the best ...

HANCOCK, N.H. — Anyone faced with the task of building a freestanding pile of spheres quickly discovers an obvious solution: Start by laying out the densest possible two-dimensional packing and then ...

In 1611 German mathematician Johannes Kepler made a conjecture about the densest way to stack oranges or other spheres with a minimum of space between them. It seemed nothing could beat the standard ...