![]() ![]() You get the well-known value ρ = Pi/(2*sqrt(3))=0. Height = height of the rectangle ( W = 1)ĭensity ratio of total area occupied by the circles to container area (for an infinite hexagonal packing N the number of circles colors correspond to active researchers in the past, see "References" at the bottom of the page Legend: Please note that all packings (including their coordinates, of course) are normalized such that their width (i.e. Proven optimal packings are indicated by a radius in bold face type. Please use the links in the following table to view a picture for a certain configuration.įurthermore, note that for certain values of N several distinct optimal configurations exist The table below summarizes the current status of the search. Thus (very near) optimal tours are provided for every packing.Īll optimal TSP tours of all packings are stored as nice PDF files This problem is known as the "Traveling Salesman Problem" (TSP). It is useful to know a tour visiting each of the circle centers once which is of minimal length. Tip: This also works for circles, triangles. by using the linksĪll coordinates of all packings are packed as ASCII filesĪll packings are stored as nice PDF filesĪll contact graphs of all packings are stored as nice PDF filesįor industrial applications, for instance if a machine has to do an important job at every circle center, I love using square or rectangle to hide my new posts, or to simply create a cool background that moves. You may download ASCII files which contain all the values of radius, ratio etc. Unitary-radius circles Packing of unitary-radius circles in a rectangle (minimizing perimeter), Numerical results and graphics source Packing of unitary. The best known packings of equal circles in a rectangle with variable aspect ratio The best known packings of equal circles in a rectangle with variable aspect ratio (complete up to N = 500) Last update: 1ĭownload Results History of updates References Therefore the proportion of the plane covered by the circles is pi/4 0.785398ldots 78.5 to 3 significant figures. ![]()
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