Nephroid Evolute

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

The Evolute of the Nephroid given by

$\displaystyle x$	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}[3\cos t-\cos(3t)]$
$\displaystyle y$	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}[3\sin t-\sin(3t)]$

is given by

$\displaystyle x$	$\textstyle =$	$\displaystyle \cos^3 t$
$\displaystyle y$	$\textstyle =$	$\displaystyle {\textstyle{1\over 4}}[3\sin t+\sin(3t)],$

which is another Nephroid.