The Rational Distance Problem for Equilateral Triangles

2017/03/20 by Barbara, Roy
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1703.06866

Abstract

Let (P) denote the problem of existence of a point in the plane of a given triangle T, that is at rational distance from all the vertices of T. In this article, we provide a complete solution to (P) for all equilateral triangles.

Related

• The Rational Distance Problem for Isosceles Triangles with one rational side
• Points at Rational Distance from the Vertices of a Unit Polygon
• Points at rational distances from the vertices of certain geometric objects
• Several special cases of a square problem
• A unique pair of triangles