Let $S$ be the unit sphere in $\Bbb R^3$ with centre $(0, 0, 0)$

$\sigma(u, v) = (\cos v/\cosh u,\sin v/\cosh u,\tanh u)$

is a parametrization of $S$ minus the north and south poles.

Show that meridians and parallels on $S$ correspond under $\sigma$ to perpendicular straight lines in the plane with coordinates $(u, v)$.

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    $\begingroup$ What are your thoughts on this question ? $\endgroup$ – Yves Daoust Apr 1 at 18:57

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