EntityQ994401· pop 10· linked from 19 articlesfour-vertex theoremSign in to savetheorem that every simple closed smooth curve in the plane has at least four points of locally extreme curvatureConnectionscurveEntitymaxima and minimaEntitygeometryEntityInternational Standard Book NumberEntitycircleEntityreal numberEntitymathematical proofEntityradiusEntitydigital object identifierEntityellipseEntitycontinuous functionEntityJSTOROrganizationtangentEntityQ118398Entityfundamental theorem of algebraEntitymultiplicative inverseEntityif and only ifEntityconvex setEntitycurvatureEntitynormEntityCategoriesPolygonsTheorems about curvesTheorems in differential geometryTheorems in discrete geometry