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The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.
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 ]
A diagram showing circles packing in a square packing arrangement. Date: 25 February 2009: Source: Own work: Author: Inductiveload: Permission (Reusing this file) Own work, all rights released (Public domain) Other versions
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The circle packing theorem states that a circle packing exists if and only if the pattern of adjacencies forms a planar graph; it was originally proved by Paul Koebe in the 1930s, and popularized by William Thurston, who rediscovered it in the 1970s and connected it with the theory of conformal maps and conformal geometry. [1]
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English: An illustration of the circle packing theorem on the planar graph of K 5 (the complete graph on five vertices) minus one edge. The positions and colors of the vertices in the top graph and the circles in the bottom drawing correspond; any two vertices with an edge between them in the top graph have their corresponding circles touching at a tangent in the bottom drawing.