# Rational Distance Problem

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Is there a point at rational distances from the vertices of a unit square? This unsolved question is known as the rational distance problem [1, 2].

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Contributed by: Ed Pegg Jr (June 2016)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The ellipse has 193 of the triples (or 386 counting reflections in ), with inverse points on the cubic .

References

[1] R. K. Guy, "Rational Distances from the Corner of a Square," in *Unsolved Problems in Number Theory*, 2nd ed., New York: Springer-Verlag, 1994 pp. 181–185.

[2] Wikipedia. "Unit Square." (May 26, 2016) en.wikipedia.org/wiki/Unit_square.

[3] S. Kurz. "Heronian Figures." (May 26, 2016) www.wm-archive.uni-bayreuth.de/index.php?id=554&L=3.

## Permanent Citation

"Rational Distance Problem"

http://demonstrations.wolfram.com/RationalDistanceProblem/

Wolfram Demonstrations Project

Published: June 1 2016