Shephard's Problem
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High Quality Content by WIKIPEDIA articles! In mathematics, Shephard's problem is the following geometrical question: if K and L are centrally symmetric convex bodies in n-dimensional Euclidean space such that whenever K and L are projected onto a hyperplane, the volume of the projection of K is smaller than the volume of the projection of L, then does it follow that the volume of K is smaller than that of L. In this case, "centrally symmetric" means that the reflection of K in the origin, K, is a translate of K, and similarly for L. If k : Rn k is a projection of Rn onto some k-dimensional…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, Shephard's problem is the following geometrical question: if K and L are centrally symmetric convex bodies in n-dimensional Euclidean space such that whenever K and L are projected onto a hyperplane, the volume of the projection of K is smaller than the volume of the projection of L, then does it follow that the volume of K is smaller than that of L. In this case, "centrally symmetric" means that the reflection of K in the origin, K, is a translate of K, and similarly for L. If k : Rn k is a projection of Rn onto some k-dimensional hyperplane k (not necessarily a coordinate hyperplane) and Vk denotes k-dimensional volume, Shephard's problem is to determine the truth or falsity of the implication.