Applications of The Circle Packing Theorem
The circle packing theorem is a useful tool to study various problems in planar geometry, conformal mappings and planar graphs. An elegant proof of the planar separator theorem, originally due to Lipton and Tarjan, has been obtained in this way. Another application of the circle packing theorem is that unbiased limits of bounded-degree planar graphs are almost surely recurrent. Other applications include implications for the cover time. and estimates for the largest eigenvalue of bounded-genus graphs.
Circle packing has also become an essential tool in origami design, as each appendage on an origami figure requires a circle of paper. Robert J. Lang has used the mathematics of circle packing to develop computer programs that aid in the design of complex origami figures.
In graph drawing, circle packing has been used to find drawings of planar graphs with bounded angular resolution and with bounded slope number.
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