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:
“The human body is not a thing or substance, given, but a continuous creation. The human body is an energy system ... which is never a complete structure; never static; is in perpetual inner self-construction and self-destruction; we destroy in order to make it new.”
—Norman O. Brown (b. 1913)