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