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This provides a new perspective and some generalisations to the problem of interpolation with increasingly flat radial basis functions. When the evaluation points are fixed and unisolvent, we show that the worst-case optimal method converges to a polynomial method. In an additional one-dimensional extension, we allow also the points to be selected optimally and show that in this case convergence is to the unique Gaussian quadrature\u2013type method that achieves the maximal polynomial degree of exactness. 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