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In mathematics, a convex body in -dimensional Euclidean space is a compact convex set with non-empty interior. Some authors do not require a non-empty interior ...
Radon's theorem - on convex sets, that any set of d + 2 points in R d can be partitioned into two disjoint sets whose convex hulls intersect; Separating axis theorem; Shapley–Folkman lemma - a result in convex geometry with applications in mathematical economics that describes the Minkowski addition of sets in a vector space
The main result of the paper is a randomized algorithm for finding an approximation to the volume of a convex body in -dimensional Euclidean space by assuming the existence of a membership oracle. The algorithm takes time bounded by a polynomial in n {\displaystyle n} , the dimension of K {\displaystyle K} and 1 / ε {\displaystyle 1 ...
In combinatorial geometry, the Hadwiger conjecture states that any convex body in n-dimensional Euclidean space can be covered by 2 n or fewer smaller bodies homothetic with the original body, and that furthermore, the upper bound of 2 n is necessary if and only if the body is a parallelepiped. There also exists an equivalent formulation in ...
In convex geometry, the Mahler volume of a centrally symmetric convex body is a dimensionless quantity that is associated with the body and is invariant under linear transformations. It is named after German-English mathematician Kurt Mahler .
In general, computing the John ellipsoid of a given convex body is a hard problem. However, for some specific cases, explicit formulas are known. Some cases are particularly important for the ellipsoid method. [5]: 70–73 Let E(A, a) be an ellipsoid in , defined by a matrix A and center a.
Dive team recovers body at site of Baltimore bridge collapse as search continues for 3 others
The intersection body IK of K is defined similarly, as the star body such that for any vector u the radial function of IK from the origin in direction u is the (n – 1)-dimensional volume of the intersection of K with the hyperplane u ⊥. Equivalently, the radial function of the intersection body IK is the Funk transform of the radial ...