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Pointed distributed over a sphere

Source: Iran PPCE 2008

December 29, 2008
geometry3D geometrysphereprobability and stats

Problem Statement

Prove that we can put Ω(1ϵ) \Omega(\frac1{\epsilon}) points on surface of a sphere with radius 1 such that distance of each of these points and the plane passing through center and two of other points is at least ϵ \epsilon.
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