General position is an arrangement of points with no three collinear, or of lines with no three concurrent.

In -dimensional Euclidean space, affine general position means that no points lie in a common hyperplane. In the study of rational distances, general position may additionally require that no points lie on a common hypersphere (Qiu 2026). For points in the plane, this stronger convention excludes both collinear triples and concyclic quadruples.

See also

Concurrent, Near-Pencil, Ordinary Line, Rational Distances

Explore with Wolfram|Alpha

References

Guy, R. K. "Unsolved Problems Come of Age." Amer. Math. Monthly 96, 903-909, 1989.Qiu, J. "Infinite Rational Distance Sets in Affine General Position: Constructions in Every Dimension." 24 Aug 2026. https://arxiv.org/abs/2608.23529.

Referenced on Wolfram|Alpha

General Position

Cite this as:

Weisstein, Eric W. "General Position." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeneralPosition.html

Subject classifications