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:
“[The Republican Party] consists of those who, believing in the doctrine that mankind are capable of governing themselves and hating hereditary power as an insult to the reason and an outrage to the rights of men, are naturally offended at every public measure that does not appeal to the understanding and to the general interest of the community.”
—James Madison (1751–1836)
“There is a certain relief in change, even though it be from bad to worse; as I have found in travelling in a stage- coach, that it is often a comfort to shift one’s position and be bruised in a new place.”
—Washington Irving (1783–1859)