The constructive Jordan curve theorem

This paper presents a constructive treatment of the Jordan curve theorem. It is shown that, given a Jordan curve, and a point whose distance to the curve is positive, then there is a finite procedure to decide whether the point is inside or outside the curve. Also, given two points that are either both inside, or both outside, the curve, then there is a finite procedure that constructs a polygonal path joining the two points, that is bounded away from the curve. Finally, a finite procedure is given for constructing a point inside the curve.