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 ...

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 ...

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 ...

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, ...

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 ...

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 ...

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 ...

This news release is available in German. 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 ...