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Many puzzle books as well as mathematical journals contain articles on packing problems. Links to various MathWorld articles on packing; MathWorld notes on packing squares. Erich's Packing Center; www.packomania.com A site with tables, graphs, calculators, references, etc. "Box Packing" by Ed Pegg, Jr., the Wolfram Demonstrations Project, 2007.
Mathematical analysis of 2D packing of circles (2022). H C Rajpoot from arXiv "The best known packings of equal circles in a circle (complete up to N = 2600)" "Online calculator for "How many circles can you get in order to minimize the waste?"
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.
This additional constraint on the packing, together with the need to minimize the Coulomb energy of interacting charges leads to a diversity of optimal packing arrangements. The upper bound for the density of a strictly jammed sphere packing with any set of radii is 1 – an example of such a packing of spheres is the Apollonian sphere packing.
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 ]
Best-fit is an online algorithm for bin packing. Its input is a list of items of different sizes. Its output is a packing - a partition of the items into bins of fixed capacity, such that the sum of sizes of items in each bin is at most the capacity. Ideally, we would like to use as few bins as possible, but minimizing the number of bins is an ...
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