Numerical ranges and Poncelet curves Original Research Article

Convex circuits which have the property of circles of The Great Poncelet Theorem are introduced. The circuits are generated as boundaries of numerical ranges of specially constructed matrices. Algebraic and geometric properties of such matrices and their numerical ranges are obtained. These properties lead to a new proof of the Poncelet Theorem. The proposed approach illustrates the fact that complex relations between geometrical figures in a plane may have simple interpretation in a space of higher dimension.