In mathematics, a convex body in n-dimensional Euclidean space Rn is a compact convex set with non-empty interior.
A convex body K is called symmetric if it is centrally symmetric with respect to the origin, i.e. a point x lies in K if and only if its antipode, −x, also lies in K. Symmetric convex bodies are in a one-to-one correspondence with the unit balls of norms on Rn.
Important examples of convex bodies are the Euclidean ball, the hypercube and the cross-polytope.
Famous quotes containing the word body:
“They threw off their clothes, and he gathered her to him, and found her, found the pure lambent reality of her for ever invisible flesh. Quenched, inhuman, his fingers upon her unrevealed nudity were the fingers of silence upon silence, the body of mysterious night upon the body of mysterious night, the night masculine and feminine, never to be seen with the eye, or known with the mind, only known as a palpable revelation of living otherness.”
—D.H. (David Herbert)