A geometric inequality for circle packings

Pablo A. Parrilo; Ronen Peretz

doi:10.1007/s00454-003-2880-2

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arXiv · math/0205278

A geometric inequality for circle packings

Pablo A. Parrilo·Ronen Peretz

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Abstract

A geometric inequality among three triangles, originating in circle packing problems, is introduced. In order to prove it, we reduce the original formulation to the nonnegativity of a particular polynomial in four real indeterminates. Techniques based on sum of squares decompositions, semidefinite programming, and symmetry reduction are then applied to provide an easily verifiable nonnegativity certificate.

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Pablo A. Parrilo, Ronen Peretz. 2002-05-27. A geometric inequality for circle packings. https://doi.org/10.1007/s00454-003-2880-2

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