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  2. Circle packing - Wikipedia

    en.wikipedia.org/wiki/Circle_packing

    In the two-dimensional Euclidean plane, Joseph Louis Lagrange proved in 1773 that the highest-density lattice packing of circles is the hexagonal packing arrangement, [1] in which the centres of the circles are arranged in a hexagonal lattice (staggered rows, like a honeycomb), and each circle is surrounded by six other circles.

  3. Circle packing in a circle - Wikipedia

    en.wikipedia.org/wiki/Circle_packing_in_a_circle

    Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle. Table of solutions, 1 ≤ n ≤ 20 [ edit ]

  4. Circle packing in a square - Wikipedia

    en.wikipedia.org/wiki/Circle_packing_in_a_square

    Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square. Equivalently, the problem is to arrange n points in a unit square aiming to get the greatest minimal separation, d n , between points. [ 1 ]

  5. Circular uniform distribution - Wikipedia

    en.wikipedia.org/wiki/Circular_uniform_distribution

    Densities for > are normalised to the maximum density, those for = and are scaled to aid visibility. The sample mean of a set of N measurements z n = e i θ n {\displaystyle z_{n}=e^{i\theta _{n}}} drawn from a circular uniform distribution is defined as:

  6. List of centroids - Wikipedia

    en.wikipedia.org/wiki/List_of_centroids

    The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.

  7. Characteristic length - Wikipedia

    en.wikipedia.org/wiki/Characteristic_length

    In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.

  8. Radial distribution function - Wikipedia

    en.wikipedia.org/wiki/Radial_distribution_function

    This equation is only valid in the sense of distributions, since () is not normalized: () =, so that () diverges as the volume , leading to a Dirac peak at the origin for the structure factor. Since this contribution is inaccessible experimentally we can subtract it from the equation above and redefine the structure factor as a regular function:

  9. 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.