Abstract: Plane closed polygons are harmonically analysed, i.e., they are expressed in the form of the sum of fundamental $k-$regular polygons. From this point of view Napoleon's theorem and its generalization, the so-called theorem of Petr, are studied. By means of Petr's theorem the fundamental polygons of an arbitrary polygon have been found geometrically.
Keywords: finite Fourier series, polyon transformation
Classification (MSC2000): 51M20
Full text of the article will be available in end of 2002.