Points at Rational Distance from the Vertices of a Unit Polygon

2009/12/15 by Roy Barbara, Barbara, Roy
Computer Science · Mathematics · #11R32 #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #Point processes and geometric inequalities #math.NT #msc:11R32

paper · pdf · doi:10.48550/arxiv.0912.2981

5 pages

openalex publication_date 2009/12/15 · arxiv created 2009/12/16 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the existence of a point in the plane of a unit polygon, that is at rational distance from each vertex of the polygon. A negative answer is obtained in almost all cases.

Related

• The Rational Distance Problem for Equilateral Triangles
• Points at rational distances from the vertices of certain geometric objects
• Several special cases of a square problem
• The Rational Distance Problem for Isosceles Triangles with one rational side
• Other special cases of a square problem