General position is an arrangement of points with no three collinear , or of lines with
no three concurrent .
In 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
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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 https://mathworld.wolfram.com/GeneralPosition.html
Subject classifications
-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.
