University of Tennessee
Here is the observation (by Peter Doyle) underlying the talk; you might try your hand at the easy-when-you-see-it proof:
Suppose a and b are positive real numbers. Show that six circles of successive radii {a, b, b/a, 1/a, 1/b, a/b} will exactly close up when placed tangent to one another around a circle of radius 1. (See the picture).
From this simple start we will see how a whole world of spiral circle packings, Descartes ovals, and related geometry opens up. I think the ancient Greeks would have felt right at home with this topic --- except for the computer experiments, of course.
Ken Stephenson is a leader in the area of circle packings: creating, manipulating and interpreting configurations of circles with preassigned tangency patterns. If you'd like more information, see "Circle Packing: A Mathematical Tale", Notices of the AMS, Vol 50, no.11, Dec. 2003, 1376-1388 (cover article).
