Editing Carathéodory's theorem (convex hull) (section)

== Example ==
[[Image:Caratheodorys theorem example.svg|thumb|280px|An illustration of Carathéodory's theorem for a square in '''R'''<sup>2</sup>]]
Carathéodory's theorem in 2 dimensions states that we can construct a triangle consisting of points from ''P'' that encloses any point in the convex hull of ''P''.

For example, let ''P'' = {(0,0), (0,1), (1,0), (1,1)}. The convex hull of this set is a square. Let ''x'' = (1/4, 1/4) in the convex hull of ''P''. We can then construct a set {(0,0),(0,1),(1,0)} = {{italics correction|''P''}}&prime;, the convex hull of which is a triangle and encloses ''x.''