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8 Feb 2024: c) Consider a parametrisation of S2 {(0, 0, 1)} as a surface of revolution, i.e.σ(u, v) =. (f(u) cos v, f(u) sin v, g(u). )with WLOG ... Σ K dA. (a) The torus given by the image of σ(u, v) =((a b cos u) cos v, (a b cos u) sin v, sin u. ).

15 Apr 2024: 2π sin r and bounds a disc of area 2π(1 cos r).(b) For the Poincaré disc model (D, gD), and r (0, ), show that each circle C(p, r) ... b) Show that the map T from the Möbius group to C given by.