= Center of symmetry
{title2=$S=2\mathbf c-S$}
A point $\mathbf c$ is a center of symmetry of a <set> $S$ in <Euclidean space> if <point reflection> $\mathbf x\mapsto2\mathbf c-\mathbf x$ maps $S$ onto itself. Every <ellipse> has its <center of an ellipse> as a center of symmetry. More generally, a nonempty bounded <set> has at most one: two such reflections compose to translation by twice the difference of their centers, and iterating a nonzero translation contradicts boundedness.
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