Mathematicians have long known that it’s possible to pack at most 12 identical spheres around and touching a 13th. Dodecahedron. In 1943, Hungarian mathematician L. Fejes Tóth conjectured that the ...

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 ...

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 ...

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 ...

Liquid bridges: wet packing of disks at 3.1% liquid content. The tomography image on the left is the raw data after noise reduction. The processed image on the right shows the spheres in blue and the ...

SOME automatic and continuous coal-weighing apparatus make use of the experimental fact that graded-to-size coal weighs the same per unit volume whatever the size of the lumps; hence a cubic foot of ...