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Like the diameter, the width can be computed using the method of rotating calipers. [4] The diameter and width are equal only for a body of constant width. Every set of bounded diameter in the Euclidean plane is a subset of a body of constant width with the same diameter. [9]
Diameter If (M, d) is a metric space and S is a subset of M, the diameter of S is the supremum of the distances d(x, y), where x and y range over S. Discrete metric The discrete metric on a set X is the function d : X × X → R such that for all x, y in X, d(x, x) = 0 and d(x, y) = 1 if x ≠ y. The discrete metric induces the discrete ...
The diameter of a set is the least upper bound of the set of all distances between pairs of points in the subset. A different and incompatible definition is sometimes used for the diameter of a conic section: any chord which passes through the conic's centre. A diameter of an ellipse is any line passing through the centre of the ellipse. [2]
Diameter (graph theory), the longest distance between two vertices of a graph; Diameter (group theory), the maximum diameter of a Cayley graph of the group; Equivalent diameter, the diameter of a circle or sphere with the same area, perimeter, or volume as another object; Kinetic diameter, a measure of particles in a gas related to the mean ...
So the diameter of is bounded by +. Lemma: A closed subset of a compact set is compact. Let K be a closed subset of a compact set T in R n and let C K be an open cover of K. Then U = R n \ K is an open set and = {} is an open cover of T.
Subspace, a particular subset of a parent space; A subset of a topological space endowed with the subspace topology; Linear subspace, in linear algebra, a subset of a vector space that is closed under addition and scalar multiplication
Credit - Photograph by Platon for TIME. P resident-elect Donald Trump, TIME’s 2024 Person of the Year, sat down for a wide-ranging interview at his Mar-a-Lago Club in Palm Beach, Fla., on Nov ...
The collection of convex subsets of a vector space, an affine space, or a Euclidean space has the following properties: [9] [10] The empty set and the whole space are convex. The intersection of any collection of convex sets is convex. The union of a sequence of convex sets is convex, if they form a non-decreasing chain for inclusion.