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:
“When we say that pleasure is the end, we do not mean the pleasure of the profligate or that which depends on physical enjoyment—as some think who do not understand our teachings, disagree with them, or give them an evil interpretation—but by pleasure we mean the state wherein the body is free from pain and the mind from anxiety.”
—Epicurus (c. 341–271 B.C.)