Select three points a, b, and c, randomly with respect to the surface of an n-sphere. These three points determine a fourth, x, which is the intersection of the sphere with the axis perpendicular to the abc plane. (Choose the pole nearest the plane.) I could have, just as easily, selected x, a distance d from x, and three points d units away from x. The distribution of d is not uniform, but that's ok. For every x and d, the three points abc form an acute triangle with probability pn-1?. By induction, pn? = 1/4.

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