  We provide a self contained proof of a result of Dudley [Dud64]} which shows
that a bounded convex-body in $\Re^d$ can be $\varepsilon$-approximated, by the
intersection of $O_d\bigl(\varepsilon^{-(d-1)/2} \bigr)$ halfspaces, where
$O_d$ hides constants that depends on $d$.
