Uh-oh, you’ve encountered a math problem. If you followed an internal link, drop me a note. Otherwise, how did you get here?

  1. Show that the densest packing of circular cylinders of any aspect ratio in Euclidean 3-space is the same as the circle packing density in the plane (or construct a counterexample).

  2. Show that the sphere, of all convex centrally symmetric bodies, minimizes the maximum packing density in Euclidean 3-space. It would even be nice to show that a minimizer exists.