Mathematical Digest
Short Summaries of Articles about Mathematics in the Popular Press"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, MarchApril 2003, pages 181182. 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' twentyyear 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
