**
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: habdelmoez@yahoo.com

email: pech@pf.jcu.cz

**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.**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2001 ELibM for
the EMIS Electronic Edition
*