# Meridians and Parallels on a Unit Sphere

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 $$(u, v)$$.

• What are your thoughts on this question ? – Yves Daoust Apr 1 at 18:57