Archimedean spiral
= Archimedean spiral
{c}
{title2=$r=a+b\theta$}
{wiki}
= Archimedes' spiral
{c}
{synonym}
An Archimedean spiral has radius linear in polar angle, $r=a+b\theta$. For the special parametrization $(u\cos u,u\sin u)$, the <curvature of a plane curve> is $(u^2+2)/(1+u^2)^{3/2}$. Its parameter speed is $\sqrt{1+u^2}$, so it remains a <regular curve> at the origin.