| 单词 | Rational Distances |
| 释义 | Rational DistancesIt is possible to find six points in the Plane, no three on a Line and no four on a Circle (i.e., none ofwhich are Collinear or Concyclic), such that all the mutual distances are Rational. An example is illustrated by Guy (1994, p. 185). It is not known if a Triangle with Integer sides, Medians, and Area exists(although there are incorrect Proofs of the impossibility in the literature). However, R. L. Rathbun,A. Kemnitz, and R. H. Buchholz have showed that there are infinitely many triangles with Rationalsides (Heronian Triangles) with two RationalMedians (Guy 1994, p. 188). See also Collinear, Concyclic, Cyclic Quadrilateral, Equilateral Triangle, Euler Brick,Heronian Triangle, Rational Quadrilateral, Rational Triangle, Square, Triangle
Guy, R. K. ``Six General Points at Rational Distances'' and ``Triangles with Integer Sides, Medians, and Area.'' §D20 and D21 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 185-190, 1994. |
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