Sphere Packing
The third part of the problem asks for the densest sphere packing or packing of other specified shapes. Although it expressly includes shapes other than spheres, it is generally taken as equivalent to the Kepler conjecture.
American mathematician Thomas Callister Hales has given a computer-aided proof of the Kepler conjecture. It shows that the most space-efficient way to pack spheres is in a pyramid shape.
Read more about this topic: Hilbert's Eighteenth Problem
Famous quotes containing the words sphere and/or packing:
“Everything goes, everything comes back; eternally rolls the wheel of being. Everything dies, everything blossoms again; eternally runs the year of being. Everything breaks, everything is joined anew; eternally the same house of being is built. Everything parts, everything greets every other thing again; eternally the ring of being remains faithful to itself. In every Now, being begins; round every Here rolls the sphere There. The center is everywhere. Bent is the path of eternity.”
—Friedrich Nietzsche (1844–1900)
“The good husband finds method as efficient in the packing of fire-wood in a shed, or in the harvesting of fruits in the cellar, as in Peninsular campaigns or the files of the Department of State.”
—Ralph Waldo Emerson (1803–1882)