Carathéodory's Fundamental Theorem

Each point in the convex hull of a set S in R^n is in the convex combination of n+1 or fewer points of S.

See also

Convex Hull, Helly's Theorem

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Eckhoff, J. "Helly, Radon, and Carathéodory Type Theorems." Ch. 2.1 in Handbook of Convex Geometry (Ed. P. M. Gruber and J. M. Wills). Amsterdam, Netherlands: North-Holland, pp. 389-448, 1993.

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Carathéodory's Fundamental Theorem

Cite this as:

Weisstein, Eric W. "Carathéodory's Fundamental Theorem." From MathWorld--A Wolfram Web Resource.

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