Grégoire Nicollier, Convolution filters for triangles,
Forum Geometricorum, 13 (2013) 61--85.
Abstract. The construction of a new triangle by erecting similar ears on the sides of a given triangle (as in Napoleon's theorem) can be considered as the convolution of the initial triangle with another triangle. We use the discrete Fourier transformation and a shape function to give a complete and explicit description of such convolution filters and their iterates. Our method leads to many old and new results in a very direct way.
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