The Rational Distance Problem for Equilateral Triangles

Roy Barbara, Antoine Karam


We provide a complete characterization of all equilateral triangles \(T\) for which there exists a point in the plane of \(T\), that is at rational distance from each vertex of \(T\).


Equilateral triangle; Rational distance problem; Bi-quadric number; Legendre’s symbol; Non-degenerated triangle; Primitive integral triangle

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