In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occupied by spheres – that can be achieved by a regular lattice arrangement is
The same packing density can also be achieved by alternate stackings of the same close-packed planes of spheres, including structures that are aperiodic in the stacking direction. The Kepler conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular. This conjecture is now widely considered proven by T. C. Hales.
Many crystal structures are based on a close-packing of atoms, or of large ions with smaller ions filling the spaces between them. The cubic and hexagonal arrangements are very close to one another in energy, and it may be difficult to predict which form will be preferred from first principles.
Read more about Close-packing Of Equal Spheres: Fcc and Hcp Lattices, Lattice Generation, Miller Indices
Famous quotes containing the words equal and/or spheres:
“The new concept of the child as equal and the new integration of children into adult life has helped bring about a gradual but certain erosion of these boundaries that once separated the world of children from the word of adults, boundaries that allowed adults to treat children differently than they treated other adults because they understood that children are different.”
—Marie Winn (20th century)
“It launch’d forth filament, filament, filament, out of itself,
Ever unreeling them, ever tirelessly speeding them.
And you O my soul where you stand,
Surrounded, detached, in measureless oceans of space,
Ceaselessly musing, venturing, throwing, seeking the spheres to connect them,
Till the bridge you will need be form’d, till the ductile anchor hold,
Till the gossamer thread you fling catch somewhere, O, my soul.”
—Walt Whitman (1819–1892)