## packingA way to place objects of the same kind so that they touch in some specified way, often inside a container with specified properties. The objects to be packed may be polyhedra, polygons, spheres, ellipsoids, hyperspheres, or any other type of shape, and the number of dimensions involved may range from two upwards. The fraction of a space filled by a given collection of objects is called the packing density. The densest packing of circles in
the plane is the hexagonal lattice of the bee's honeycomb, which has a packing
density of 0.9069 ... In 1611, Johannes Kepler
proposed that hexagonal, or face-centered cubic, packing is also the densest
possible way to arrange spheres in three dimensions – an assertion
known as Kepler's conjecture.
Currently, the worst known convex packer
in two-dimensions is the smoothed octagon, with a packing density of about
0.902. Stanislaw Ulam conjectured that the
sphere was the worst packing object in three-dimensional space. ## Related entries• cannonball problem• moving sofa problem • Slothouber-Graatsma puzzle ## Related category• GEOMETRY | |||||

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