Back Vierscheitelsatz German Teorema de los cuatro vértices Spanish Théorème des quatre sommets French 4-정점 정리 Korean Teorema dos quatro vértices Portuguese Теорема о четырёх вершинах Russian Izrek o štirih temenih Slovenian Теорема про чотири вершини Ukrainian 四頂點定理 Chinese
In geometry, the four-vertex theorem states that the curvature along a simple, closed, smooth plane curve has at least four local extrema (specifically, at least two local maxima and at least two local minima). The name of the theorem derives from the convention of calling an extreme point of the curvature function a vertex. This theorem has many generalizations, including a version for space curves where a vertex is defined as a point of vanishing torsion.