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.
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Nicollier, G. Convolution filters for polygons and the Petr–Douglas–Neumann theorem. Beitr Algebra Geom 54, 701–708 (2013). https://doi.org/10.1007/s13366-013-0143-9
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DOI: https://doi.org/10.1007/s13366-013-0143-9
Keywords
- Petr–Douglas–Neumann theorem
- Napoleon’s theorem
- Convolution filter for polygons
- Shape function
- Discrete Fourier transformation