  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.

Algebraic Geometry;Optimization and Control