The Pursuit of Perfect Packing, Second Edition

by Weaire; Denis

• ISBN13: 9781420068177
• ISBN10: 1420068172
• Edition: 2nd
• Format: Hardcover
• Copyright: 2008-03-10
• Publisher: CRC Press

Summary

Coauthored by one of the creators of the most efficient space packing solution, the Weairea??Phelan structure, The Pursuit of Perfect Packing, Second Editionexplores 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, Vorono?? decomposition, and Delaunay decomposition, as well as actual structure models, such as the Kelvin cell and the Weairea??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, thisaccessible 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

Preface to First Edition	p. xi
Preface to Second Edition	p. xiii
How Many Sweets in the Jar?	p. 1
Loose Change and Tight Packing	p. 5
A Teasing But Tractable Problem	p. 5
A Handful of Coins	p. 5
Order and Disorder	p. 8
Hard Problems with Hard Spheres	p. 11
The Greengrocer's Dilemma	p. 11
Ordered Close Packing-The Kepler Problem	p. 11
The Kepler Conjecture	p. 14
Marvelous Clarity, Neurotic Anxiety: The Life of Kepler	p. 16
Progress by Leaps and Bounds?	p. 18
Proof Positive?	p. 21
News from the Western Front	p. 21
The Programme of Thomas Hales	p. 23
At Last?	p. 25
Polishing Off the Programme	p. 29
The Acceptance of Proof	p. 30
The Flyspeck Project	p. 32
Who Cares?	p. 33
The Power of Thought	p. 33
Disordered Packings	p. 35
Balls in Bags	p. 35
A New Way of Looking	p. 37
How Many Balls in the Bag?	p. 38
Is the Bernal Close Packing Well Defined?	p. 39
Bernal's Long-Running Ball Game	p. 39
Tomography Takes Over	p. 40
Sands and Grains	p. 43
Granular Materials	p. 43
Osborne Reynolds: A Footprint in the Sand	p. 44
Major Bagnold's Desert Drive	p. 47
Dunes	p. 49
Order from Shaking	p. 51
Segregation	p. 53
Granular Temperature	p. 55
Divide and Conquer: Tiling Space	p. 57
Packing and Tiling	p. 57
The Voronoi Construction	p. 58
The Dual Construction of Delaunay	p. 60
Applications	p. 60
Vertices in Tilings	p. 61
Three Dimensions	p. 61
Regular and Semiregular Packings	p. 62
Peas and Pips	p. 67
Vegetable Staticks	p. 67
Stephen Hales	p. 69
Pomegranate Pips	p. 70
Biological Cells, Lead Shot, Rubber Balls, and Soap Bubbles: Plus ca Change	p. 71
Enthusiastic Admiration: The Honeycomb	p. 75
The Honeycomb Problem	p. 75
What the Bees Do Not Know	p. 78
A Search for Structure	p. 81
A Voice in the Wilderness	p. 81
The Two-Dimensional Soap Froth	p. 82
The Rules of the Game	p. 83
In a Cambridge Garden	p. 85
Toils and Troubles with Bubbles	p. 87
Playing with Bubbles	p. 87
A Blind Man in the Kingdom of the Sighted	p. 88
Proving Plateau	p. 91
Foam and Ether	p. 93
The Kelvin Cell	p. 97
Most Beautiful and Regular	p. 98
The Twinkling of an Eye	p. 99
Simulated Soap	p. 100
A Discovery in Dublin	p. 101
Crystals of Small Bubbles	p. 104
Bubbles in Beijing	p. 107
An Olympian Vision	p. 107
Fun and Fit for Purpose?	p. 107
A Flexible Friend?	p. 108
The Architecture of the World of Atoms	p. 111
Molecular Tactics	p. 111
Atoms and Molecules: Begging the Question	p. 113
Atoms as Points	p. 115
Playing Hardball	p. 116
Modern Crystallography	p. 120
Crystalline Packings	p. 121
Packing Tetrahedra	p. 123
Changed Utterly: Quasicrystals	p. 125
Amorphous Solids	p. 128
Crystal Nonsense	p. 129
Apollonius and Concrete	p. 131
Mixing Concrete	p. 131
Apollonian Packing	p. 132
Packing Fraction and Fractal Dimension	p. 136
Packing Fraction in Granular Aggregates	p. 136
Packings and Kisses in High Dimensions	p. 139
Packing in Many Dimensions	p. 139
A Kissing Competition	p. 143
Kissing the Neighbors in Higher Dimensions	p. 143
Will Disorder Win in the End?	p. 144
The Sweets in the Jar, the Pebbles on the Beach...	p. 147
Those Sweets	p. 147
Hey, What Shape Do You Want Your Ice Cubes?	p. 148
Another Walk on the Beach	p. 148
The Giant's Causeway	p. 151
Worth Seeing?	p. 151
Idealization Oversteps Again	p. 152
The First Official Report	p. 153
Mallett's Model	p. 155
A Modern View	p. 156
The Last Word?	p. 156
Lost City?	p. 157
Finite Packings and Tessellations, from Soccer to Sausages	p. 159
The Challenge of a Finite Suitcase	p. 159
Soccer Balls	p. 159
Golf Balls	p. 160
Buckyballs	p. 161
Buckminster Fuller	p. 163
Graphenes	p. 164
The Thomson Problem	p. 164
Packing Points on a Disk	p. 167
The Tammes Problem	p. 168
Universal Optimal Configurations	p. 169
Helical Packings	p. 170
Virus Architecture	p. 171
Stuffing Sausages	p. 173
Filling Boxes	p. 174
The Malfatti Problem	p. 176
Odds and Ends	p. 179
Ordered Loose Packings	p. 179
Parking Cars	p. 179
Goldberg Variations	p. 181
Packing Regular Pentagons	p. 182
Dodecahedral Packing and Curved Spaces	p. 182
Microspheres and Opals	p. 184
Protein Folding	p. 186
The Tetra Pak Story	p. 186
Packing Regular Tetrahedra	p. 188
Nature and Geometry	p. 189
The Best Packing in Two Dimensions	p. 191
When Equal Shares Are Best	p. 191
Turning Down the Heat: Simulated Annealing	p. 195
Index	p. 197
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