We discuss the electrodynamics of slowly rotating metamaterials as observed in their rest frame of reference, and present a corresponding first order polarizability theory. A formulation governing the response of an arbitrary array of scatterers to excitation under rotation is provided and used to explore the rotation footprint properties, whith applications to non-reciprocal dynamics, rotation sensors and optical gyroscopes. The metamaterial sensitivity to rotation is rigorously defined, and the associated physical mechanisms are exposed. These can be intimately related to two century-old problems in number theory: the no-three-in-line problem, and the Heilbronn triangle problem. New arrays, base on Erdős solution to the former, are proposed. It is shown that structures inspired by Erdős solution may achieve rotation sensitivities that outperform that of the Sagnac loop gyroscope.
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