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 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 ...

It’s a tight squeeze. Mathematicians have proved that they know the best way to pack spheres in 8 and 24 dimensions – the first time this problem has been solved in a new dimension in almost 20 years.

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 ...

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American Earlier this year, Maryna Viazovska showed ...

Circle packing encapsulates the challenge of optimally arranging a set of circles within a given container without overlap, a process that has profound implications in both theoretical mathematics and ...

Improvements in how densely spheres and other shapes can be packed together could lead to advances in materials science, deep space communication and theoretical physics. In the lead-up to the launch ...