Coauthored by one of the creators of the most efficient space packing solution, the Weaire–Phelan structure, The Pursuit of Perfect Packing, Second Edition
explores a problem of importance in physics, mathematics, chemistry, biology, and engineering: the packing of structures. Maintaining its mathematical core, this edition continues and revises some of the stories from its predecessor while adding several new examples and applications.
The book focuses on both scientific and everyday problems ranging from atoms to honeycombs. It describes packing models, such as the Kepler conjecture, Voronoï decomposition, and Delaunay decomposition, as well as actual structure models, such as the Kelvin cell and the Weaire–Phelan structure. The authors discuss numerous historical aspects and provide biographical details on influential contributors to the field, including emails from Thomas Hales and Ken Brakke.
With examples from physics, crystallography, engineering, and biology, this accessible and whimsical book touches on many aspects of packing objects. It will help you understand components of packing and aid you in the quest for the perfect packing solution.
Table of Contents
How Many Sweets in the Jar?
Loose Change and Tight Packing
A Teasing but Tractable Problem
A Handful of Coins
Order and Disorder
Hard Problems with Hard Spheres
The Greengrocer’s Dilemma
Ordered Close Packing—The Kepler Problem
The Kepler Conjecture
Marvelous Clarity, Neurotic Anxiety: The Life of Kepler
Progress by Leaps and Bounds?
News from the Western Front
The Programme of Thomas Hales
Polishing Off the Programme
The Acceptance of Proof
The Flyspeck Project
The Power of Thought
Balls in Bags
A New Way of Looking
How Many Balls in the Bag?
Is the Bernal Close Packing Well Defined?
Bernal’s Long-Running Ball Game
Tomography Takes Over
Sands and Grains
Osborne Reynolds: A Footprint in the Sand
Major Bagnold’s Desert Drive
Order from Shaking
Divide and Conquer: Tiling Space
Packing and Tiling
The Voronoï Construction
The Dual Construction of Delaunay
Vertices in Tilings
Regular and Semiregular Packings
Peas and Pips
Biological Cells, Lead Shot, Rubber Balls, and Soap Bubbles: Plus ça Change
Enthusiastic Admiration: The Honeycomb
The Honeycomb Problem
What the Bees Do Not Know
A Search for Structure
A Voice in the Wilderness
The Two-Dimensional Soap Froth
The Rules of the Game
In a Cambridge Garden
Toils and Troubles with Bubbles
Playing with Bubbles
A Blind Man in the Kingdom of the Sighted
Foam and Ether
The Kelvin Cell
Most Beautiful and Regular
The Twinkling of an Eye
A Discovery in Dublin
Crystals of Small Bubbles
Bubbles in Beijing
An Olympian Vision
Fun and Fit for Purpose?
A Flexible Friend?
The Architecture of the World of Atoms
Atoms and Molecules: Begging the Question
Atoms as Points
Changed Utterly: Quasicrystals
Apollonius and Concrete
Packing Fraction and Fractal Dimension
Packing Fraction in Granular Aggregates
Packings and Kisses in High Dimensions
Packing in Many Dimensions
A Kissing Competition
Kissing the Neighbors in Higher Dimensions
Will Disorder Win in the End?
The Sweets in the Jar, the Pebbles on the Beach
Hey, What Shape Do You Want Your Ice Cubes?
Another Walk on the Beach
The Giant’s Causeway
Idealization Oversteps Again
The First Official Report
A Modern View
The Last Word?
Finite Packings and Tessellations, from Soccer to Sausages
The Challenge of a Finite Suitcase
The Thomson Problem
Packing Points on a Disk
The Tammes Problem
Universal Optimal Configurations
The Malfatti Problem
Odds and Ends
Ordered Loose Packings
Packing Regular Pentagons
Dodecahedral Packing and Curved Spaces
Microspheres and Opals
The Tetra Pak Story
Packing Regular Tetrahedra
Nature and Geometry
Appendix A: The Best Packing in Two Dimensions
Appendix B: Turning Down the Heat: Simulated Annealing
". . . entertaining and easy to read . . ."
– Bill Satzer, 3M Company, in MAA Online, September 2008
"The book by Aste and Weaire gives in 20 chapters an elementary survey on this and other packing problems that are of importance in physics, mathematics, chemistry, biology, and engineering . . . accessible to a wide spectrum of readers."
– Michal Krížek, in Applications of Mathematics, 2008, Vol. 53, No. 6