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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 ]
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.
The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere. The counterparts of a circle in other dimensions can never be packed with complete efficiency in dimensions larger than one (in a one-dimensional universe, the circle analogue is just two points). That is ...
The final part of the book concerns a conjecture of William Thurston, proved by Burton Rodin and Dennis Sullivan, that makes this analogy concrete: conformal mappings from any topological disk to a circle can be approximated by filling the disk by a hexagonal packing of unit circles, finding a circle packing that adds to that pattern of ...
Circle packing in an equilateral triangle is a packing problem in discrete mathematics where the objective is to pack n unit circles into the smallest possible equilateral triangle. Optimal solutions are known for n < 13 and for any triangular number of circles, and conjectures are available for n < 28 .
Example of the circle packing theorem on K − 5, the complete graph on five vertices, minus one edge. We say that two circles drawn in a plane kiss (or osculate) whenever they intersect in exactly one point. A "coin graph" is a graph formed by a set of circles, no two of which have overlapping interiors, by making a vertex for each circle and ...
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.
Circle packing in a right isosceles triangle is a packing problem where the objective is to pack n unit circles into the smallest possible isosceles right triangle. Minimum solutions (lengths shown are length of leg) are shown in the table below. [ 1 ]