In 1611, Johannes Kepler—known for his laws of planetary motion—offered a solution to the question concerning the densest possible way to arrange equal-sized spheres. The famed astronomer took on this problem when asked how to stack cannonballs so as to take up the least amount of space. Kepler concluded that the best configuration is a so-called face-centered cubic lattice—an approach commonly used in grocery stores for displaying oranges: Every cannonball should rest in the cavity left by the four cannonballs (lined up in a tight, two-by-two square) lying directly below it. This was merely a conjecture, however, that was not proven until almost 400 years later by a University of Michigan mathematician.In 1611, Johannes Kepler—known for his laws of planetary motion—offered a solution to the question concerning the densest possible way to arrange equal-sized spheres. The famed astronomer took on this problem when asked how to stack cannonballs so as to take up the least amount of space. Kepler concluded that the best configuration is a so-called face-centered cubic lattice—an approach commonly used in grocery stores for displaying oranges: Every cannonball should rest in the cavity left by the four cannonballs (lined up in a tight, two-by-two square) lying directly below it. This was merely a conjecture, however, that was not proven until almost 400 years later by a University of Michigan mathematician.[#item_full_content]