Theorem of Jordan

The Jordan Curve Theorem states that any simple, closed curve on a plane—like a circle or an oval—divides the plane into exactly two regions: an inside and an outside. No matter how the curve is drawn, as long as it doesn’t intersect itself, it creates a clear boundary that separates the two areas. This means you can walk around the curve and move from one region to the other only by crossing the boundary. The theorem underpins many concepts in geometry, topology, and computer graphics, confirming that closed, non-intersecting loops always partition the plane into two distinct parts.