Samir Hanna Safar

An Elementary Proof of Inscribed Squares for Smooth Curves via the H-Shape Construction

We give a new, elementary proof that every C² Jordan curve in the plane inscribes at least one square. The existence of inscribed squares on smooth curves has been known since the work of Schnirelman (1929, 1944), and Stromquist (1989) extended the result to C¹ curves. Our contri...