High Quality Content by WIKIPEDIA articles! In mathematics, Minkowski's theorem is the statement that any convex set in Rn which is symmetric with respect to the origin and with volume greater than 2n d(L) contains a non-zero lattice point. The theorem was proved by Hermann Minkowski in 1889 and became the foundation of the branch of number theory called the geometry of numbers.Suppose that L is a lattice of determinant d(L) in the n-dimensional real vector space Rn and S is a convex subset of Rn that is symmetric with respect to the origin, meaning that if x is in S then ?x is also in S. Minkowski's theorem states that if the volume of S is strictly greater than 2n d(L), then S must contain at least one lattice point other than the origin.

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