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:
“There has always been the same amount of light in the world. The new and missing stars, the comets and eclipses, do not affect the general illumination, for only our glasses appreciate them.”
—Henry David Thoreau (1817–1862)
“The Americans are violently oral.... That’s why in America the mother is all-important and the father has no position at all—isn’t respected in the least. Even the American passion for laxatives can be explained as an oral manifestation. They want to get rid of any unpleasantness taken in through the mouth.”
—W.H. (Wystan Hugh)