 Solution

ID: past-exam-of-the-geometry-course-of-the-university-of-oxford/2011/3/c/ii/solution

r_{u} = (f^{'} cos v, f^{'} sin v, 1), r_{v} = (- f sin v, f cos v, 0) .

The mixed inner product vanishes, giving

I = (1 + f^{'} (u)^{2}) d u^{2} + f (u)^{2} d v^{2} .

Taking

f (u) = cosh u

cosh^{2} u

, as used in the parent calculation.

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