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Abstract: A drumhead of which shape produces the lowest possible sound among all drumheads of given area? An answer to this simplest problem of geometric optimization of eigenvalues is given by the Rayleigh-Faber-Krahn inequality, stating that the optimal shape here is the disc. Different problems of geometric optimization for eigenvalues of the Laplacian on Euclidean domains and of its cousin, Laplace-Beltrami operator on surfaces, will be discussed.