The constructive Jordan curve theorem

1975/06/01 by G. Berg, William H. Julian, Ray Mines +1 · 3 citations
Mathematics · Medicine · #Algebra over a field #Calculus (dental) #Computer science #Constructive #Mathematics #Mathematics and Applications #Medicine #Orthodontics #Process (computing) #Programming language #Pure mathematics

paper · pdf · doi:10.1216/rmj-1975-5-2-225

openalex publication_date 1975/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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. AMS (MOS) subject classifications (1970). Primary 02E05, 57A05.

Cited by

• The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic
• Computing conformal maps onto circular domains
• Jordan curve theorem [wikipedia]