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sphere packing

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The arranging of non-overlapping spheres in space

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an arrangement of non-overlapping spheres within a containing space
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In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space.
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He introduced Blichfeldt's principle and Blichfeldt's upper bound on the density of sphere packings.
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Let me try to destroy your confidence in your intuition for sphere packing.
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Modular forms appear in other areas, such as algebraic topology, sphere packing, and string theory.
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The Kepler conjecture states that no sphere packing can have greater density than this.
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Sphere Packing The number is of fundamental importance in mathematics, physics, and chemistry.
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In short, there is no such thing as ‘the’ densest sphere packing.
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Generalisations can be made to higher dimensions – this is called sphere packing, which usually deals only with identical spheres.
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A typical sphere packing problem is to find an arrangement in which the spheres fill as large a proportion of the space as possible.
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For a lattice packing the kissing number is the same for every sphere, but for an arbitrary sphere packing the kissing number may vary from one sphere to another.
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Gray also lists the 18th problem as "open" in his 2000 book, because the sphere-packing problem (also known as the Kepler conjecture) was unsolved, but a solution to it has now been claimed.
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However, sphere packing problems can be generalised to consider unequal spheres, n-dimensional Euclidean space (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space.
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Kepler explained the snowflake’s symmetric form in terms of packing spheres together in space.
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According to Kepler, there is no denser way to pack spheres in space.
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For those feeling really ambitious, what about packing spheres in three-dimensional regions?
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This process is based on the use of selenium-coated spheres in a packed bed.
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Ceramic packing, in particular saddle packing, rings, spheres
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What is the most efficient way to pack identical spheres in space?
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I couldn’t help glancing across at the neighbouring pillar, with its densely packed blue sphere.
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There are two common metallic structures that correspond to the closest possible packing of spheres of constant size.
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So for this packing, the spheres fill slightly less than three quarters of the space.
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Ceramic catalyst carriers, in particular porous ceramic packing, saddle packing, rings, spheres
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Kepler’s thoughts about flat layers of spheres suggest starting with circle packings in a plane.
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The crystal structure contains toluene molecules packed between the spheres of the fullerene.
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However, for some simple models of porous media, permeability can be calculated (e.g., random close packing of identical spheres).
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