Library/Geometry/Combinatorial geometry/Packings

Packings

Overview
Important

In combinatorial geometry, a packing is an arrangement of non-overlapping objects (usually congruent shapes) inside a given region. The main questions are: What is the maximum number of objects that can fit? Or, what is the densest possible arrangement?

Important properties

  • Packings can be regular (following a repeating pattern) or irregular.

  • The density of a packing is the fraction of the space covered by the shapes.

  • Some packings are optimal, meaning no denser arrangement is possible.

  • Packings can be studied in two or more dimensions (e.g., circles in a plane, spheres in space).