From Analog to Digital or How to make the Perfect Poppy-Seed Bagel

Topic

The problem of distributing a large number of points uniformly over the surface of a sphere has not only inspired mathematical researchers, it has attracted the attention of biologists, chemists, and physicists working in such fields as viral morphology, crystallography, molecular structure, and electrostatics. In two dimensions, the analogous problem is simply that of uniformly distributing points on the circumference of a disk, and equally spaced points provide an obvious answer. So we are faced with this question: What sets of points on a sphere imitate the role of the roots of unity on the unit circle? We will discuss answers to this question as well as to analogous questions for uniformly distributing points on more general surfaces such as the torus (bagel).