Nephroid Involute

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

The Involute of the Nephroid given by

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

beginning at the point where the nephroid cuts the y-Axis is given by

$\displaystyle x$	$\textstyle =$	$\displaystyle 4\cos^3 t$
$\displaystyle y$	$\textstyle =$	$\displaystyle 3\sin t+\sin(3t),$

another Nephroid. If the Involute is begun instead at the Cusp, the result is Cayley's Sextic.