MathDB
Miklos Schweitzer 1982_7

Source: geometry

January 31, 2009
geometry3D geometrysphereadvanced fieldsadvanced fields unsolved

Problem Statement

Let V V be a bounded, closed, convex set in Rn \mathbb{R}^n, and denote by r r the radius of its circumscribed sphere (that is, the radius of the smallest sphere that contains V V). Show that r r is the only real number with the following property: for any finite number of points in V V, there exists a point in V V such that the arithmetic mean of its distances from the other points is equal to r r. Gy. Szekeres
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