This paper generalizes the Napoleon–Barlotti theorem, showing that centers of constructed polygons form a regular n-gon.
The Napoleon–Barlotti theorem belongs to the family of theorems related to the Petr–Douglas–Neumann theorem. The Napoleon–Barlotti theorem states: On the sides of an affine-regular n-gon construct regular n-gons. Then the centers of these regular n-gons form a regular n-gon. In the paper we give a generalization of this theorem.
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Blažek et al. (2025) studied this question.
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