Some Theorems on Polygons with One-line Spectral Proofs release_xycqb33ryrfalfiupj6g4hadum

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 Bar-lotti theorem, the Petr-Douglas-Neumann theorem, and other theorems as an exercise.
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