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Packing circles in simple bounded shapes is a common type of problem in recreational mathematics. The influence of the container walls is important, and hexagonal packing is generally not optimal for small numbers of circles. Specific problems of this type that have been studied include: Circle packing in a circle; Circle packing in a square
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 ]
Circle packings, as studied in this book, are systems of circles that touch at tangent points but do not overlap, according to a combinatorial pattern of adjacencies specifying which pairs of circles should touch. The circle packing theorem states that a circle packing exists if and only if the pattern of adjacencies forms a planar graph; it ...
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 ]
This category groups articles relating to the packing of circles in planes, on spheres, and on other types of surfaces, both with the aim of high packing density (circle packing) and with specified combinatorial patterns of tangencies (circle packing theorem).
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).
The rhombitrihexagonal tiling can be used as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with four other circles in the packing (kissing number). [4] The translational lattice domain (red rhombus) contains six distinct circles.
A circle packing for a five-vertex planar graph. The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose interiors are disjoint. A circle packing is a connected collection of circles (in general, on any Riemann surface) whose interiors are ...