Each point in the convex hull of a set 
in 
is in the convex combination of 
or fewer points of 
.
Carathéodory's Fundamental Theorem
See also
Convex Hull, Helly's TheoremExplore with Wolfram|Alpha
References
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.Referenced on Wolfram|Alpha
Carathéodory's Fundamental TheoremCite this as:
Weisstein, Eric W. "Carathéodory's Fundamental Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CaratheodorysFundamentalTheorem.html