Two-dimensional surfaces that can be made by rolling up a sheet of paper are called developable surfaces. Find the geodesic equations on the following developable surfaces and solve the equations.

(a) A circular cylinder of radius \(R\), using coordinates \(\theta\) and \(z\).

(b) A circular cone of half-angle \(\alpha\) (which is the angle between the cone and the axis of symmetry) using coordinates \(\theta\) and \(\ell\), where \(\ell\) is the distance of a point on the cone from the apex. Hint: Find the distance \(d s\) between nearby points on the surface in terms of \(\ell, \alpha, d \theta\), and \(d \ell\).