How to stack oranges in 24 dimensions

摘要

It's a tight squeeze. Mathematicians have proved that they know the best way to pack spheres in eight and 24 dimensions - the first time this problem has been solved in a new dimension for almost 20 years. "I think they're fantastic results. I'm excited that this has been done at last," says Thomas Hales at the University of Pittsburgh, Pennsylvania. The sphere-packing problem asks a deceptively simple question: what arrangement crams the most spheres into a limited volume? It is easy to describe, but difficult to prove. In 1611, Johannes Kepler suggested that the best arrangement for 3-dimensional spheres like oranges is a pyramid. But it took until 1998 for Hales to publish a proof - and another 16 years to formally verify it.