Grégoire Nicollier, Some theorems on polygons with one-line spectral proofs,
Forum Geometricorum, 15 (2015) 267--273.

Abstract. We use discrete Fourier transforms and convolution products to give one - line proofs of some theorems about planar polygons. We illustrate the method by computing the perspectors of a pair of concentric equilateral triangles constructed from a hexagon and leave the proofs of Napoleon's theorem, the Barlotti theorem, the Petr - Douglas - Neumann theorem, and other theorems as an exercise.

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