= Homothetic convex bodies
{title2=$B=v+sA,\quad s>0$}
Two <convex bodies> are <homothetic convex bodies> if one is a <translation> of a positive <uniform dilation> of the other. Their <lengths> scale by $s$ and their <volumes> by $s^n$. Closed <disks> of positive <radii> are <homothetic convex bodies>; axis-aligned positive-sided <rectangles> are <homothetic convex bodies> exactly when their aspect ratios agree. The <Brunn-Minkowski theorem> characterizes this relation by equality of root-volumes in <Minkowski addition>.
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