ABSTRACT
The Jordan Curve Theorem states that every simple (i.e., does not cross itself) closed curve in the Euclidean plane divides the plane into two regions-the part that lies outside the curve, and the part that lies inside it. (It is named after the French mathematician Camille Jordan (1838-1922), who is also known for bringing Galois theory into the mainstream and drawing attention to its importance.) The theorem is one of those results that seems completely obvious, yet is extraordinarily difficult to prove. Figure 1, produced using techniques described in [1] and [2], displays a Jordan Curve of Jordan.
