In algebraic geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the general case situation, as opposed to some more special or coincidental cases that are possible. Its precise meaning differs in different settings.
For example, generically, two lines in the plane intersect in a single point (they are not parallel or coincident). One also says "two generic lines intersect in a point", which is formalized by the notion of a generic point. Similarly, three generic points in the plane are not colinear – if three points are collinear (even stronger, if two coincide), this is a degenerate case.
This notion is important in mathematics and its applications, because degenerate cases may require an exceptional treatment; for example, when stating general theorems or giving precise statements thereof, and when writing computer programs (see generic complexity).
Read more about General Position: General Linear Position, More Generally, Different Geometries, General Type, Other Contexts, Abstractly: Configuration Spaces
Famous quotes containing the words general and/or position:
“A general loathing of a gang or sect usually has some sound basis in instinct.”
—Ezra Pound (1885–1972)
“Being in a family is like being in a play. Each birth order position is like a different part in a play, with distinct and separate characteristics for each part. Therefore, if one sibling has already filled a part, such as the good child, other siblings may feel they have to find other parts to play, such as rebellious child, academic child, athletic child, social child, and so on.”
—Jane Nelson (20th century)