For a cylinder of radius r and two points P1 and P2 on it, the geodesic on the cylinder connecting P1 to P2 is the curve on the cylinder of least length joining P1 to P2. Show that the length of the geodesic on the cylinder with axis the w-axis and radius r that joins two points (r, θ1, w1) and (r, θ2, w2) is
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