Examples for

Packing & Covering Problems

Packing and covering problems are special optimization problems concerning geometric objects in a given space or region. Many of the problems involve arranging geometric objects (usually identical) into the space or region as densely as possible with no overlap. Wolfram|Alpha can find the best-known solutions for many two-dimensional packing problems. It can also do estimations for packing/covering with everyday‐life objects.

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Geometric Packing in 2D

Optimize the packing of common 2D geometric figures into a given area.

Compute properties of a geometric packing:

pack 24 circles in a circle

Specify dimensions of the container:

pack 9 squares in a triangle of side 10

Specify dimensions of packed objects:

pack squares of side 3in into a circle of diameter 2ft

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Packing & Covering of Objects

Estimate the number of objects required to pack or cover another object.