\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose $R$ is the region in the plane
enclosed by $y=x^2$ and $y=4$.

\medskip

\noindent a) Compute the perimeter $P$ and area $A$ of $R$, and then
compute the
ratio $Q=A/P^2$.

\medskip

\noindent {\bf Note} By squaring the perimeter the ratio becomes
independent of the units chosen to measure the region.

\medskip

\noindent b) Compute this ratio $Q=A/P^2$ for these four regions: the
region $R$, a square, a circle, and an equilateral triangle. Draw the
figures in increasing order of $Q$.

\vfil\eject\end