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  2. Close-packing of equal spheres - Wikipedia

    en.wikipedia.org/wiki/Close-packing_of_equal_spheres

    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 lattice packing is

  3. Sphere packing - Wikipedia

    en.wikipedia.org/wiki/Sphere_packing

    Here there is a choice between separating the spheres into regions of close-packed equal spheres, or combining the multiple sizes of spheres into a compound or interstitial packing. When many sizes of spheres (or a distribution) are available, the problem quickly becomes intractable, but some studies of binary hard spheres (two sizes) are ...

  4. Random close pack - Wikipedia

    en.wikipedia.org/wiki/Random_close_pack

    Random close packing (RCP) of spheres is an empirical parameter used to characterize the maximum volume fraction of solid objects obtained when they are packed randomly. For example, when a solid container is filled with grain, shaking the container will reduce the volume taken up by the objects, thus allowing more grain to be added to the container.

  5. Circle packing - Wikipedia

    en.wikipedia.org/wiki/Circle_packing

    A compact binary circle packing with the most similarly sized circles possible. [7] It is also the densest possible packing of discs with this size ratio (ratio of 0.6375559772 with packing fraction (area density) of 0.910683). [8] There are also a range of problems which permit the sizes of the circles to be non-uniform.

  6. Wikipedia : Featured picture candidates/Close-packed spheres

    en.wikipedia.org/.../Close-packed_spheres

    This yields the greatest possible packing density and the lowest energy state. — — Below is a candidate caption for use in Close-packing article, added 16:33, 26 February 2007 (and revised 20:15, 26 February 2007) — — Shown above is what the science of sphere packing calls a closest-packed arrangement.

  7. 10 Hard Math Problems That Even the Smartest People in the ...

    www.aol.com/10-hard-math-problems-even-150000090...

    A packed bunch of spheres will have an average kissing number, which helps mathematically describe the situation. But a basic question about the kissing number stands unanswered.

  8. Kepler conjecture - Wikipedia

    en.wikipedia.org/wiki/Kepler_conjecture

    Diagrams of cubic close packing (left) and hexagonal close packing (right). Imagine filling a large container with small equal-sized spheres: Say a porcelain gallon jug with identical marbles. The "density" of the arrangement is equal to the total volume of all the marbles, divided by the volume of the jug.

  9. Finite sphere packing - Wikipedia

    en.wikipedia.org/wiki/Finite_sphere_packing

    In mathematics, the theory of finite sphere packing concerns the question of how a finite number of equally-sized spheres can be most efficiently packed. The question of packing finitely many spheres has only been investigated in detail in recent decades, with much of the groundwork being laid by László Fejes Tóth.