Two points $A$ and $B$ are located on the curved surface of the circular cylinder of radius $R$ with axis along the $z$-axis. We denote their locations by $\left(R, \phi_{A}, z_{A}\right)$ and $\left(R, \phi_{B}, z_{B}\right)$ using cylindrical polar coordinates and assume $\phi_{A} \neq \phi_{B}, z_{A} \neq z_{B}$. A path $\phi(z)$ is drawn on the cylinder to join $A$ and $B$. Show that the path of minimum distance between the points $A$ and $B$ is a helix, and determine its pitch. [For a helix with axis parallel to the $z$ axis, the pitch is the change in $z$ after one complete helical turn.]