Let the diameter of the convex body $K$ be $c.$ It's easy to see that if the convex body is symmetric, then the convex body belongs to a ball $B(y,c/2).$ This bound is sharp in every dimension. But what if the convex body is not symmetric? Are the sharp bounds known for every dimension for $K \subset B(y,a)$? Second question: The unique extremal case must be the simplex? So what is the smallest ball that includes the standard simplex?
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1https://en.wikipedia.org/wiki/Jung%27s_theorem – Theo Bendit Sep 20 '23 at 07:45