On the Construction of Regular Polygons and Generalized Napoleon Vertices
نویسندگان
چکیده
An algebraic foundation for the derivation of geometric construction schemes transforming arbitrary polygons with n vertices into k-regular n-gons is given. It is based on circulant polygon transformations and the associated eigenpolygon decompositions leading to the definition of generalized Napoleon vertices. Geometric construction schemes are derived exemplarily for different choices of n and k.
منابع مشابه
Napoleon Polygons
An n-gon is called Napoleon if the centers of the regular ngons erected outwardly on its sides are vertices of a regular n-gon. In this note we obtain a new geometric characterization of Napoleon ngons and give a new proof of the well-known theorem of Barlotti Greber ([1], [3]) that an n-gon is Napoleon if and only if it is affine regular. Moreover, we generalize this theorem by obtaining an an...
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