Radon's Theorem

Any set of n+2 points in R^n can always be partitioned in two subsets V_1 and V_2 such that the convex hulls of V_1 and V_2 intersect.

See also

Convex Hull

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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.McMullen, P. and Shepard, G. C. Convex Polytopes and the Upper Bound Conjecture. London: Cambridge University Press, pp. 22-24, 1971.Peterson, B. B. "The Geometry of Radon's Theorem." Amer. Math. Monthly 79, 949-963, 1972.Peyerimhoff, N. "Areas and Intersections in Convex Domains." Amer. Math. Monthly 104, 697-704, 1997.Rado, R. "Theorems on the Intersection of Convex Sets of Points." J. London Math. Soc. 27, 320-328, 1952.Ziegler, G. M. Ex. 6.0 in Lectures on Polytopes. New York: Springer-Verlag, 1994.

Referenced on Wolfram|Alpha

Radon's Theorem

Cite this as:

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

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