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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. No reason to believe densest packing must be periodic, but periodic packings come arbitrarily close to the maximum density. Calculate optimal circle arrangements and packing densities.

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Interactive circle packing tool to visualize optimal arrangements of circles within various container shapes In a periodic packing, spheres are not restricted to just the corners of a fundamental cell Perfect for designers, mathematicians, and educators.

The obvious square packing is optimal for 1, 4, 9, 16, 25, and 36 circles (the six smallest square numbers), but ceases to be optimal for larger squares from 49 onwards.

The probably densest irregular packing ever found by computers and humans, of course, like andré müller Square packing is a packing problem where the objective is to determine how many congruent squares can be packed into some larger shape, often a square or circle. Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible.