Introduction In May of 1694, in a lecture hall at the University of Cambridge, Isaac Newton and the astronomer David Gregory started to contemplate the nature of the stars, only to end up with a math puzzle that would persist for centuries. The details of their conversation were poorly recorded and are possibly apocryphal — it had something to do with how stars of varying sizes would orbit a central sun. What’s remembered today is the more general question it inspired: Given a central sphere, ho...