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 ...

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 ...

How bees, beer cans and big data all solve the same problem: not enough space. By Steven Strogatz Photo illustrations by Jens Mortensen Each installment of “Math, Revealed” starts with an object, ...

As a simple physics model for crystal and quasicrystal formation, the Hertzian potential describes the interaction between two soft-core colloidal particles. However, explaining why quasicrystals ...

With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history. How to safely reopen offices, ...

Winter means tangerines. The joy of sitting in a warm room and peeling tangerines until your fingers turn yellow is a luxury that can only be savored in winter. As I was eating tangerines, I looked at ...

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 ...

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 ...

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematicians have been studying for centuries. Sphere packing might seem ...