Cardioid Evolute

$\begin{figure}\begin{center}\BoxedEPSF{CardioidEvolute.epsf scaled 700}\end{center}\end{figure}$

$\displaystyle x$	$\textstyle =$	$\displaystyle {\textstyle{2\over 3}}a +{\textstyle{1\over 3}}a\cos\theta(1-\cos\theta)$
$\displaystyle y$	$\textstyle =$	$\displaystyle {\textstyle{1\over 3}} a\sin\theta(1-\cos\theta).$