The Four-Vertex Theorem
The Four-Vertex Theorem
A simple, closed, plane curve of class [latex]C^2[/latex] has at least four vertices.
Simple indicates that the curve has no self-intersections.
Specifically, there are at least two points at which the curvature takes a minimum value and at least two points where it takes a maximum value.
This theorem immediately implies that an ellipse has at least four vertices.
