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## Homework Statement

Find the geodesics on a cone of infinite height, [itex]x^{2}+y^{2} = \tan{\alpha}^{2}z^{2}[/itex] using polar coordinates [itex](x,y,z)=(r\cos{\psi},r\sin{\psi},z) with z=r\tan(\alpha)[/itex]

## The Attempt at a Solution

I am not sure with how should I expres the element [itex]dz^{2}[/itex] ? When it is a function of α (My calculus was always weak especially stuff with creating a derivative by dividing...)

Thanks.