A closed embedded smooth plane curve has at least four vertices, where a vertex is defined as an extremum of curvature.
Four-Vertex Theorem
See also
CurvatureExplore with Wolfram|Alpha
References
Tabachnikov, S. "The Four-Vertex Theorem Revisited--Two Variations on the Old Theme." Amer. Math. Monthly 102, 912-916, 1995.Referenced on Wolfram|Alpha
Four-Vertex TheoremCite this as:
Weisstein, Eric W. "Four-Vertex Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Four-VertexTheorem.html