Four-vertex theorem

The Four-Vertex Theorem is a result in differential geometry and the study of curves. It states that for a simple, closed, smooth curve in the plane (which means a curve that does not intersect itself and is continuously differentiable), there are at least four distinct points at which the curvature of the curve attains a local maximum or minimum. To elaborate, curvature is a measure of how sharply a curve bends at a given point.