Abstract. We use the discrete Fourier transformation of planar polygons, convolution filters, and a shape function to give a very simple and enlightening description of circulant polygon transformations and their iterates. We consider in particular Napoleon's and the Petr-Douglas-Neumann theorem.
We characterize affinely regular polygons in a real affine space as follows. Consider two polygons P and Q with the same number of vertices and a common side, P being an affine image of some (convex or nonconvex) regular polygon. Q is then an affine image of the same regular polygon if and only if the vectors between the corresponding vertices of P and Q are uniquely determined multiples of the vector between the vertices just after the common side.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.