We consider two random sequential packing processes in which spheres of unit radius are randomly attached to the surface of a fixed unit sphere. Independent random spheres are generated and added ...

Imagine placing oranges or tennis balls into a rigid container. How can the balls be arranged such that they occupy the largest volume fraction of the container, otherwise known as the largest packing ...

A NUMERICAL approach using a digital computer has been used to construct a simple model of the unit cell in a randomly packed bed of identical hard spheres. The cell is built up by introducing spheres ...

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 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, ...

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 ...

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 ...

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 ...

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 ...