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Consider a symmetric convex body $A$ in $R^d$. Now, we draw another object, $A'$, concentric and translated with respect to A and having radius slightly greater than twice to the radius of $A$.

Now my question is that how many translated copies (upper and lower bound) of $A$ would be required to cover annulus obtained between $A$ and $A'$?

Please let me know if I am not able to put the question clearly.

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I do not get what "concentric and translated with respect to $A$" mean. Maybe explain in symbols? – Benoît Kloeckner Jun 8 '13 at 18:36
1) Centers of $A$ and $A'$ are same, and 2) $A'$ is $2+\epsilon$ times scaled to $A$ but without rotation. I hope this will help. – Ram Jun 9 '13 at 5:32

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