Editing General position (section)

== Different geometries ==
Different geometries allow different notions of geometric constraints. For example, a circle is a concept that makes sense in [[Euclidean geometry]], but not in affine linear geometry or projective geometry, where circles cannot be distinguished from ellipses, since one may squeeze a circle to an ellipse. Similarly, a parabola is a concept in affine geometry but not in projective geometry, where a parabola is simply a kind of conic. The geometry that is overwhelmingly used in algebraic geometry is projective geometry, with affine geometry finding significant but far less use.

Thus, in Euclidean geometry three non-collinear points determine a circle (as the [[circumcircle]] of the triangle they define), but four points in general do not (they do so only for [[cyclic quadrilateral]]s), so the notion of "general position with respect to circles", namely "no four points lie on a circle" makes sense. In projective geometry, by contrast, circles are not distinct from conics, and five points determine a conic, so there is no projective notion of "general position with respect to circles".