If 
is a family of more than 
bounded closed convex sets in Euclidean 
-space 
, and if every 
(where 
is the Helly number) members
of 
have at least one point in common, then
all the members of 
have at least one point in common.
Helly's Theorem
See also
Carathéodory's Fundamental Theorem, Helly NumberExplore 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
Helly's TheoremCite this as:
Weisstein, Eric W. "Helly's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HellysTheorem.html