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The harmonic analysis of polygons and Napoleon’s theorem. (English) Zbl 0991.51009
Summary: 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 are found geometrically.

##### MSC:
 51M20 Polyhedra and polytopes; regular figures, division of spaces
##### Keywords:
Napoleon’s theorem; theorem of Petr; polygon
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