Example image of eyePlorer eyePlorer map for 'Four-vertex theorem': Curvature Extrema Plane curve Vertex (curve) Contact (mathematics) If and only if Osculating circle Adolf Kneser Continuous function N-sphere Winding number Gömböc Equilateral polygon Maxima and minima Equiangular polygon Circle Circumscribed circle Adrien-Marie Legendre Augustin-Louis Cauchy Aleksandr Danilovich Aleksandrov Robert Osserman List of theorems Carathéodory conjecture Monostatic polytope