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:
“Fairy tales are loved by the child not because the imagery he finds in them conforms to what goes on within him, but because—despite all the angry, anxious thoughts in his mind to which the fairy tale gives body and specific content—these stories always result in a happy outcome, which the child cannot imagine on his own.”
—Bruno Bettelheim (20th century)