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Generalizing the Petr-Douglas-Neumann theorem on $$n$$-gons. (English) Zbl 1053.51010
The paper takes a different point of view, generalizing the PDN-theorem while using a proof method that is more elementary but necessarily simpler than existing proofs.
The following Theorem 1 is proved. Starting with an arbitrary plane polygon $$A_0$$, using triangles from a model $$n$$-gon $$Z$$, and constructing successive polygons $$A_k$$ according to the general construction rule, the polygon $$A_{n-2}$$ is similar to $$Z$$ and $$A_{n-1}$$ is a single point.

##### MSC:
 51M04 Elementary problems in Euclidean geometries 51M20 Polyhedra and polytopes; regular figures, division of spaces 52B11 $$n$$-dimensional polytopes
##### Keywords:
Petr’s theorem; Napoleon-Douglas-Neumann theorem
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