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

### Other articles related to "general position":

... circles passing through a common point M and otherwise in

**general position**, meaning that there are six additional points where exactly two of the circles ... The second theorem considers five circles in

**general position**passing through a single point M ... The third theorem consider six circles in

**general position**that pass through a single point M ...

... integer N, any sufficiently large finite set of points in the plane in

**general position**has a subset of N points that form the vertices of a convex polygon ... Let f(N) denote the minimum M for which any set of M points in

**general position**must contain a convex N-gon ... f(5) > 8 the more difficult part of the proof is to show that every set of nine points in

**general position**contains the vertices of a convex pentagon ...

**General Position**- Abstractly: Configuration Spaces

... In very abstract terms,

**general position**is a discussion of generic properties of a configuration space in this context one means properties that ... that points chosen at random will almost surely (with probability 1) be in

**general position**...

**General Position**

... A related concept in algebraic geometry is

**general position**– points are in

**general position**if they satisfy no more equations than are necessary ...

### Famous quotes containing the words position and/or general:

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—Franklin D. Roosevelt (1882–1945)

“The *general* Mistake among us in the Educating of our Children, is, That in our Daughters we take Care of their Persons and neglect their Minds; in our Sons, we are so intent upon adorning their Minds, that we wholly neglect their Bodies.”

—Richard Steele (1672–1729)