Smooth graph length range for a circular arch
= Smooth graph length range for a circular arch
{title2=$2a<l<\pi a$}
A circular arch of chord length $2a$ described as a smooth single-valued graph has radius $R>a$ and length $2R\arcsin(a/R)$, ranging strictly between $2a$ and $\pi a$. The straight-line limit has length $2a$. At the semicircle limit the endpoint slopes are infinite. Longer <circular arcs> require overhangs and cannot be graphs in this class.