Carathéodory’s theorem

Suppose a point p lies in the convex hullMathworldPlanetmath of a set Pd. Then there is a subset PP consisting of no more than d+1 points such that p lies in the convex hull of P.

For example, if a point p is contained in a convex hull of a set P2, then there are three points in P that determine the triangle containing p, provided, of course, that P contains at least three points.

Title Carathéodory’s theorem
Canonical name CaratheodorysTheorem
Date of creation 2013-03-22 13:57:43
Last modified on 2013-03-22 13:57:43
Owner bbukh (348)
Last modified by bbukh (348)
Numerical id 6
Author bbukh (348)
Entry type Theorem
Classification msc 52A20
Related topic ConvexSet