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:
“He had a wonderful talent for packing thought close, and rendering it portable.”
—Thomas Babington Macaulay (1800–1859)
“Nothing could his enemies do but it rebounded to his infinite advantage,—that is, to the advantage of his cause.... No theatrical manager could have arranged things so wisely to give effect to his behavior and words. And who, think you, was the manager? Who placed the slave-woman and her child, whom he stooped to kiss for a symbol, between his prison and the gallows?”
—Henry David Thoreau (1817–1862)
“There is commonly sufficient space about us. Our horizon is never quite at our elbows.”
—Henry David Thoreau (1817–1862)