The Pursuit of Perfect Packing, by T. Aste and D. Weaire
The Pursuit of Perfect Packing, by T. Aste and D. Weaire, Abingdon, Taylor and Francis, 2008, 200 pp., US$53.96 (hardback), ISBN 9781420068177. Scope: monograph. Level: general reader, postgraduate and specialist.
What's the best way to pack sweets in a jar, pack cells in a honeycomb, or pack pomegranate seeds in a pomegranate? These are just some of the questions addressed in this endlessly fascinating and lavishly illustrated book. Aste and Weaire take the reader on a whistlestop tour of tiling, granular materials, phylotaxis, bubbles, foams, quasicrystals, opals and sand dunes. One can learn how spheres ‘kiss’ in high dimensions and what a fractal packing conceived by Appolonius of Parga in 200 BC has to do with mixing concrete. In fact, it is the little historical nuggets, and the biographical sketches of figures such as Johannes Kepler, Desmond Bernal and Osbourne Reynolds, that make this book such a delightful and entertaining read.
A central theme of the book is the Kepler conjecture that states that the densest packing arrangement of spheres in three dimensions is the face-centred cubic (or cubic close-packed) structure which achieves the well-known packing fraction of 74%. This conjecture was only actually proved in 1998, and the proof is so complex that it fills several research papers and runs to hundreds of pages. This is rather typical of how complex the proofs can be of even straightforward statements in discrete geometry and the book explains how computer proofs and computer visualisation can contribute to this field. The Weaire–Phelan structure, co-discovered by one of the authors, is the most efficient soap bubble foam in the sense of being the partition of space into equal volumed cells with the least area of surface between them (beating the result found by Lord Kelvin), and is one such product of computer modelling. The authors are clearly chuffed to bits that this structure was used in the design of the ‘Water Cube’ at the Beijing Olympics.
In covering so much ground so quickly, some topics are inevitably treated with rather too much brevity for the reader to derive very much insight, protein folding and granular temperature being notable examples. I also thought that the verbatim cut-and-paste extracts of emails between one of the authors and several key figures in this field seemed a bit out of place and disrupted the flow of the narrative. But these minor quibbles apart, this book comes highly recommended as a humourous, informative and thoroughly enlightening read.
© 2010, S.J. Blundell