The Pursuit of Perfect Packing, Second Edition

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2008-03-10
  • Publisher: CRC Press

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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 Editionp. xi
Preface to Second Editionp. xiii
How Many Sweets in the Jar?p. 1
Loose Change and Tight Packingp. 5
A Teasing But Tractable Problemp. 5
A Handful of Coinsp. 5
Order and Disorderp. 8
Hard Problems with Hard Spheresp. 11
The Greengrocer's Dilemmap. 11
Ordered Close Packing-The Kepler Problemp. 11
The Kepler Conjecturep. 14
Marvelous Clarity, Neurotic Anxiety: The Life of Keplerp. 16
Progress by Leaps and Bounds?p. 18
Proof Positive?p. 21
News from the Western Frontp. 21
The Programme of Thomas Halesp. 23
At Last?p. 25
Polishing Off the Programmep. 29
The Acceptance of Proofp. 30
The Flyspeck Projectp. 32
Who Cares?p. 33
The Power of Thoughtp. 33
Disordered Packingsp. 35
Balls in Bagsp. 35
A New Way of Lookingp. 37
How Many Balls in the Bag?p. 38
Is the Bernal Close Packing Well Defined?p. 39
Bernal's Long-Running Ball Gamep. 39
Tomography Takes Overp. 40
Sands and Grainsp. 43
Granular Materialsp. 43
Osborne Reynolds: A Footprint in the Sandp. 44
Major Bagnold's Desert Drivep. 47
Dunesp. 49
Order from Shakingp. 51
Segregationp. 53
Granular Temperaturep. 55
Divide and Conquer: Tiling Spacep. 57
Packing and Tilingp. 57
The Voronoi Constructionp. 58
The Dual Construction of Delaunayp. 60
Applicationsp. 60
Vertices in Tilingsp. 61
Three Dimensionsp. 61
Regular and Semiregular Packingsp. 62
Peas and Pipsp. 67
Vegetable Staticksp. 67
Stephen Halesp. 69
Pomegranate Pipsp. 70
Biological Cells, Lead Shot, Rubber Balls, and Soap Bubbles: Plus ca Changep. 71
Enthusiastic Admiration: The Honeycombp. 75
The Honeycomb Problemp. 75
What the Bees Do Not Knowp. 78
A Search for Structurep. 81
A Voice in the Wildernessp. 81
The Two-Dimensional Soap Frothp. 82
The Rules of the Gamep. 83
In a Cambridge Gardenp. 85
Toils and Troubles with Bubblesp. 87
Playing with Bubblesp. 87
A Blind Man in the Kingdom of the Sightedp. 88
Proving Plateaup. 91
Foam and Etherp. 93
The Kelvin Cellp. 97
Most Beautiful and Regularp. 98
The Twinkling of an Eyep. 99
Simulated Soapp. 100
A Discovery in Dublinp. 101
Crystals of Small Bubblesp. 104
Bubbles in Beijingp. 107
An Olympian Visionp. 107
Fun and Fit for Purpose?p. 107
A Flexible Friend?p. 108
The Architecture of the World of Atomsp. 111
Molecular Tacticsp. 111
Atoms and Molecules: Begging the Questionp. 113
Atoms as Pointsp. 115
Playing Hardballp. 116
Modern Crystallographyp. 120
Crystalline Packingsp. 121
Packing Tetrahedrap. 123
Changed Utterly: Quasicrystalsp. 125
Amorphous Solidsp. 128
Crystal Nonsensep. 129
Apollonius and Concretep. 131
Mixing Concretep. 131
Apollonian Packingp. 132
Packing Fraction and Fractal Dimensionp. 136
Packing Fraction in Granular Aggregatesp. 136
Packings and Kisses in High Dimensionsp. 139
Packing in Many Dimensionsp. 139
A Kissing Competitionp. 143
Kissing the Neighbors in Higher Dimensionsp. 143
Will Disorder Win in the End?p. 144
The Sweets in the Jar, the Pebbles on the Beach...p. 147
Those Sweetsp. 147
Hey, What Shape Do You Want Your Ice Cubes?p. 148
Another Walk on the Beachp. 148
The Giant's Causewayp. 151
Worth Seeing?p. 151
Idealization Oversteps Againp. 152
The First Official Reportp. 153
Mallett's Modelp. 155
A Modern Viewp. 156
The Last Word?p. 156
Lost City?p. 157
Finite Packings and Tessellations, from Soccer to Sausagesp. 159
The Challenge of a Finite Suitcasep. 159
Soccer Ballsp. 159
Golf Ballsp. 160
Buckyballsp. 161
Buckminster Fullerp. 163
Graphenesp. 164
The Thomson Problemp. 164
Packing Points on a Diskp. 167
The Tammes Problemp. 168
Universal Optimal Configurationsp. 169
Helical Packingsp. 170
Virus Architecturep. 171
Stuffing Sausagesp. 173
Filling Boxesp. 174
The Malfatti Problemp. 176
Odds and Endsp. 179
Ordered Loose Packingsp. 179
Parking Carsp. 179
Goldberg Variationsp. 181
Packing Regular Pentagonsp. 182
Dodecahedral Packing and Curved Spacesp. 182
Microspheres and Opalsp. 184
Protein Foldingp. 186
The Tetra Pak Storyp. 186
Packing Regular Tetrahedrap. 188
Nature and Geometryp. 189
The Best Packing in Two Dimensionsp. 191
When Equal Shares Are Bestp. 191
Turning Down the Heat: Simulated Annealingp. 195
Indexp. 197
Table of Contents provided by Ingram. All Rights Reserved.

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