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:
“If men would avoid that general language and general manner in which they strive to hide all that is peculiar and would say only what was uppermost in their own minds after their own individual manner, every man would be interesting.”
—Ralph Waldo Emerson (1803–1882)
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