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:
“I wish more and more that health were studied half as much as disease is. Why, with all the endowment of research against cancer is no study made of those who are free from cancer? Why not inquire what foods they eat, what habits of body and mind they cultivate? And why never study animals in health and natural surroundings? why always sickened and in an environment of strangeness and artificiality?”
—Sarah N. Cleghorn (1976–1959)