"On the Complex Plane": Review of Indra's Pearls: The Vision of FelixKlein, by David Mumford, Caroline Series, and David Wright. Reviewed byBrian Hayes. AmericanScientist, March-April 2003, pages 181-182.
Part of the title of this book comes from a Buddhist legend concerning aninfinite net strung with an infinite number of shiny pearls. Each pearlreflects the universe, including the reflections of all the other pearls, sothat each has a sequence of nested reflections. The authors investigate themathematical version of Indra's pearls in the complex plane, specifically thelimit set of a Möbius transformation. Hayes states that the book isunusual in that it describes the authors' twenty-year long process of discoveryand "theorems, pictures and computer programs are all equally important in thisstory." (Albert Marden also wrote a review of this bookfor the January issue of the Notices.)
--- Mike Breen