Natural SciencesComputer ScienceMathematicsComputational GeometryGeometryTopologyClose-packed StructuresComputational ComplexityComputational Number TheoryGeometric ConstructionsDense PackingFace-centered Cubic LatticeFace-centered Cubic PackingFace-centered Cubic StructureGeometric PackingPackingPacking ProblemsSphere Packing
Johannes Kepler is best known for his elliptic laws of planetary motion. But mathematicians also remember him for a vexing problem in geometry: proposing—but not proving—that the densest possible packing of same-sized spheres is the arrangement familiar today to anyone who's ever admired a pyramid of oranges in a grocery store. Known to crystallographers as the face-centered cubic lattice packing, it fills a little over 74%–πsqrt18, to be precise—of space.