Let S be the unit sphere in 3-space centered at (1, 0, 0). Now transform the x- and y-coordinates like the squaring operation (x + yi) |——> (x^2-y^2) + 2xyi, i.e., define a function f: R^3 —> R^3 via f(x, y, z) = (x^2-y^2, 2xy, z) and apply this to the surface S to get a new surface: X = {(x^2-y^2, 2xy, z) | (x-1)^2 + y^2 + z^2 = 1}. The origin 0 belongs to X. What is the solid angle SA(X; 0) subtended by the surface X at the point 0 ??? ((( Meaning: Let U be any open neighborhood of 0 in X. Let A(U) denote the area on the unit sphere of the set of all outward normal unit vectors to X at a point of U. Then we define the solid angle SA(X; 0) = inf {A(U) | U is an open neighborhood of 0 in X}. ))) —Dan