What is included with this book?
Foreword | |
Acknowledgment | |
List of Symbols | |
Introduction | p. 1 |
Sphere Packings and the Sphere Packing Problem | p. 1 |
Kepler's Conjecture on Sphere Packings | p. 4 |
Density of Finite Packings without a Container and the Least Action Principle of Crystal Formation | p. 6 |
Locally Averaged Density and the Intrinsic Density of the Second Kind | p. 13 |
Main Theorems on Sphere Packings | p. 14 |
The Basics of Euclidean and Spherical Geometries and a New Proof of the Problem of Thirteen Spheres | p. 19 |
Vector Algebra and Basic Spherical Geometry | p. 20 |
Spherical Configurations, Area Estimates and a New Proof of the Impossibility of Thirteen Touching Neighbors | p. 61 |
Circle Packings and Sphere Packings | p. 83 |
The Problem of Circle Packings | p. 83 |
Sphere Packings and Crystal Formations, Kepler's Conjecture and a Least Action Principle of Crystal Formation | p. 89 |
Some Basic Ideas and Crucial Understanding which the Proofs of the Major Theorems are Based | p. 106 |
Geometry of Local Cells and Specific Volume Estimation Techniques for Local Cells | p. 123 |
Basic Geometry of Local Packings and Local Cells | p. 123 |
Technique of Volume Estimation of the Core Part | p. 138 |
Volume Estimation of a Rectilinear Slab | p. 164 |
Volume Estimation of Local Cells | p. 187 |
Estimates of Total Buckling Height | p. 201 |
The Correlation Between Buckling Heights and Area Estimates | p. 204 |
Area Estimates of Star Configurations | p. 215 |
Estimation of Total Buckling Height | p. 225 |
The Proof of the Dodecahedron Conjecture | p. 235 |
The Proof of Case 1: m = 12 | p. 236 |
The Proof of Case 2: m [is equal to or less then] 11 | p. 237 |
The Proof of Case 3: 13 [is equal to or less then] m [is equal to or less then] 15 | p. 238 |
Geometry of Type I Configurations and Local Extensions | p. 239 |
Geometry of Type I Local Packings and Type I Configurations | p. 241 |
Geometry of Local Extension | p. 300 |
The Proof of Main Theorem I | p. 327 |
The Proof of Main Theorem I for Core Packings with at Least Thirteen Close Neighbors | p. 329 |
The Proof of Main Theorem I for Core Packings with at Most Twelve Close Neighbors | p. 332 |
Retrospects and Prospects | p. 383 |
Retrospects | p. 383 |
Prospects | p. 387 |
References | p. 397 |
Index | p. 401 |
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