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:
“but as an Eagle
His cloudless thunderbolted on thir heads.
So vertue giv’n for lost,
Deprest, and overthrown, as seem’d,
Like that self-begott’n bird
In the Arabian woods embost,
That no second knows nor third,
And lay e’re while a Holocaust,
From out her ashie womb now teem’d
Revives, reflourishes, then vigorous most
When most unactive deem’d,
And though her body die, her fame survives,
A secular bird ages of lives.”
—John Milton (1608–1674)