Journal for Geometry and Graphics, Vol. 5, No. 1, pp. 13-22 (2001)

The Harmonic Analysis of Polygons and Napoleon's Theorem

Pavel Pech

Pedagogical Faculty, University of South Bohemia
Jeronymova 10, 371 15 Ceske Budejovice, Czech Republic email:

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.

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