The harmonic analysis of polygons and Napoleon’s theorem. (English) Zbl 0991.51009

Pech, Pavel

J. Geom. Graph. 5, No. 1, 13-22 (2001).

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