Most interesting of all, if you take a number x and replace it with its reciprocal 1/x, that is equivalent to flipping the sphere upside down and reflecting it in a mirror. The north pole becomes the south pole and the south pole becomes the north pole: zero becomes infinity and infinity becomes zero. It’s all built into the geometry of the sphere; 1/0=∞ and 1/∞=0. Infinity and zero are simply opposite poles on the Riemann sphere, and they can switch places in a blink. And they have equal and opposite powers. Figure 37: Lines and circles are the same.
