Packing Infinite Space
Many of these problems, when the container size is increased in all directions, become equivalent to the problem of packing objects as densely as possible in infinite Euclidean space. This problem is relevant to a number of scientific disciplines, and has received significant attention. The Kepler conjecture postulated an optimal solution for packing spheres hundreds of years before it was proven correct by Thomas Callister Hales. Many other shapes have received attention, including ellipsoids, Platonic and Archimedean solids including tetrahedra, and unequal-sphere dimers.
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Famous quotes containing the words packing, infinite and/or space:
“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)
“That man’s best works should be such bungling imitations of Nature’s infinite perfection, matters not much; but that he should make himself an imitation, this is the fact which Nature moans over, and deprecates beseechingly. Be spontaneous, be truthful, be free, and thus be individuals! is the song she sings through warbling birds, and whispering pines, and roaring waves, and screeching winds.”
—Lydia M. Child (1802–1880)
“It is not through space that I must seek my dignity, but through the management of my thought. I shall have no more if I possess worlds.”
—Blaise Pascal (1623–1662)