Cycloid
= Cycloid
{title2=$x=R(\theta-\sin\theta),\ y=R(1-\cos\theta)$}
{wiki}
A cycloid is the <plane curve> traced by a point on a circle rolling without slipping along a straight line. A parametrization with rolling radius $R$ is $x=R(\theta-\sin\theta)$, $y=R(1-\cos\theta)$; reversing the sign of $y$ reflects the curve. Its cusps occur at integer multiples of $2\pi$. A descending cycloidal arc solves the classical <brachistochrone problem>.