Astroid
= Astroid
{title2=$|x/a|^{2/3}+|y/a|^{2/3}=1$}
An astroid is the four-cusped <plane curve> parametrized by $x=a\cos^3t$, $y=a\sin^3t$ for $a>0$. It appears as the relative trajectory in the <astroid motion of a harmonic oscillator in a rotating frame>. The parametrization has zero first derivative at the cusps while remaining smooth as a function of its parameter.