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Four-Vertex Theorem

A closed embedded smooth Plane Curve has at least four vertices, where a vertex is defined as an extremum of Curvature.

See also Curvature


Tabachnikov, S. ``The Four-Vertex Theorem Revisited--Two Variations on the Old Theme.'' Amer. Math. Monthly 102, 912-916, 1995.

© 1996-9 Eric W. Weisstein