An extreme point or an extremal point in general sense is a point that belongs to the extremity of something.
In mathematics, an extreme point of a convex setS in a real vector space is a point in S which does not lie in the open line segment joining any two points of S. Intuitively, an extreme point is a "corner" of S. Compare: concave, convex. Futhermore, and extreme point x is defined as being extreme to space C if there does not exist x1, x2 where 0 < y < 1, such that x = Yx1 + (1-Y)x2, where x1 != x2
In mathematics, the term should not be confused with a similar notion of extremal point which is a point where some function attains its extremum. For example, points in the plane that have minimal or maximal X-coordinates are called extremal points in X direction. Similarly extremal points may be defined for any direction, not only in a direction of a coordinate axis.
In geography, an extreme (extremal) point is a point of land that extends farther in one direction than any other part of that land, which corresponds to the mathematical notion of extremal point in a given direction.
In graph theory, the leaf vertices of a tree are sometimes called extremal points or extremal vertices.
The mathematical notions of "extreme point" and "extremal point" are related: For a convex set defined in a Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics on Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... In mathematics, an object is convex if for any pair of points within the object, any point on the straight line segment that joins them is also within the object. ... Jump to: navigation, search A vector space (or linear space) is the basic object of study in the branch of mathematics called linear algebra. ... In mathematics, a line segment is a part of a line that is bounded by two end points. ... In geometry, concavity is a property of certain geometric figures, and in calculus, a property of certain graphs of functions. ... In mathematics, an object is convex if for any pair of points within the object, any point on the straight line segment that joins them is also within the object. ... In mathematics, particularly in calculus, a stationary point is a point on the graph of a function where the tangent to the graph is parallel to the x-axis or, equivalently, where the derivative of the function equals zero (known as a critical number). ... See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ... A coordinate axis is one of a set of vectors that defines a coordinate system. ... A diagram of a graph with 6 vertices and 7 edges. ... A tree with 6 vertices and 5 edges In graph theory, a tree is a graph in which any two vertices are connected by exactly one path. ...
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