nLab center of a regular polygon




Let 𝒫\mathcal{P} be a regular polygon in an Euclidean space n\mathbb{R}^n, and let \mathcal{E} be the subset of all points in n\mathbb{R}^n that is equidistant from all vertices of the regular polygon.

The center of the regular polygon 𝒫\mathcal{P} is the unique point pp \in \mathcal{E} such that for any other point qq \in \mathcal{E}, the distance from pp to a vertex of the polygon is less than or equal to the distance from qq to the same vertex of the polygon. The distance from the center of the regular polygon to a vertex of a regular polygon is called the circumradius of the regular polygon.

See also


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