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:
“Every body we know surrounds himself with a fine house, fine books, conservatory, gardens, equipage, and all manner of toys, as screens to interpose between himself and his guest. Does it not seem as if man was of a very sly, elusive nature, and dreaded nothing so much as a full rencontre front to front with his fellow?”
—Ralph Waldo Emerson (1803–1882)