If that strange condition, where no two lines are ever parallel, sounds familiar, it’s because we’ve been here before. It’s just the same phenomenon we saw in the projective plane, which Brunelleschi and his fellow painters used to develop the theory of perspective.* There, too, every pair of lines met. And this is no coincidence—one can prove that Riemann’s geometry of Points and Lines on a sphere is the same as that of the projective plane.
