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:
“Though I knit my brow,
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anyway.
Though I check my tongue,
this tortured face of mine
dissolves in a smile.
Though I drive my heart to hardness,
my body bears
the gooseflesh
of desire.
When I see that man,
how on earth
can my anger
survive?”
—Amaru (c. seventh century A.D.)