The Rational Distance Problem for Equilateral Triangles

Roy Barbara, Antoine Karam

Abstract


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 \(T\).


Keywords


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

Full Text:

PDF

References


T.G. Berry, Points at rational distance from the vertices of a triangle, Acta Arithmetica LXII (4) (1992), 391 – 398.

R. Barbara, The rational distance problem for polygons, Mathematical Gazette 97 (538) (2013), note 97.11.

R. Barbara and A. Karam, The rational distance problem for isosceles triangles with one rational side, Communications in Mathematics and Applications 4 (2) (2013), 169 – 179.

Wikipedia, Equilateral Triangle, https://en.wikipedia.org/wiki/Equilateral_triangle.

Wolfram Mathworld, Equilateral Triangle, http://mathworld.wolfram.com/EquilateralTraiangle.html.




DOI: http://dx.doi.org/10.26713%2Fcma.v9i2.659

Refbacks

  • There are currently no refbacks.


eISSN 0975-8607; pISSN 0976-5905