August’s featured book of the month is “Indra’s Pearls: The Vision of Felix Klein” by David Mumford, Caroline Series and David Wright.
“The book explores the patterns created by iterating conformal maps of the complex plane called Möbius transformations, and their connections with symmetry and self-similarity.
The book’s title refers to Indra’s net, a metaphorical object described in the Buddhist text of the Flower Garland Sutra. Indra’s net consists of an infinite array of gossamer strands and pearls. The frontispiece to Indra’s Pearls quotes the following description:
- In the glistening surface of each pearl are reflected all the other pearls … In each reflection, again are reflected all the infinitely many other pearls, so that by this process, reflections of reflections continue without end.
The allusion to Felix Klein’s “vision” is a reference to Klein’s early investigations of Schottky groups and hand-drawn plots of their limit sets. It also refers to Klein’s wider vision of the connections between group theory, symmetry and geometry.”
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