Format:
Online-Ressource
,
v.: digital
Edition:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
9781461411291
Content:
Jeffrey C. Lagarias
Content:
The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of three-dimensional Euclidean space by equal spheres is attained by the "cannonball" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use of computers. This book centers around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, pu
Note:
Description based upon print version of record
,
The Kepler Conjecture; Preface; Part I: Introduction and Survey; Part II: Proof of the Kepler Conjecture; Part III: A Revision to the Proof of the Kepler Conjecture; Part IV: Initial Papers of the Hales Program; Contents; Part I: Introduction and Survey; Introduction to Part I; 1 The Kepler Conjecture and Its Proof, by J. C. Lagarias; Contents; The Kepler Conjecture and Its Proof; 1 The Kepler Problem for Sphere Packing; 2 Why the Kepler Problem Is Difficult; 3 Local Density Approach: History; 4 Hales Program and Hales-Ferguson Papers; 5 Peer-Reviewing of the Hales-Ferguson Papers
,
6 Reliability of the Hales-Ferguson Proof7 Formal Proof of the Kepler Conjecture; 8 Applications of the Hales-Ferguson Proof Methodology; 9 Contents of This Volume; PART I. Survey: Local Density Inequalities for Sphere Packing; PART II. Proof: Hales-Ferguson Proof of the Kepler Conjecture; PART III. Revision: A revision of the proof of the Kepler Conjecture; PART IV. Prehistory: Initial Hales papers on the Kepler Conjecture; Acknowledgements; References; 2 Bounds for Local Density of Sphere Packings and the Kepler Conjecture, by J. C. Lagarias; Contents
,
Bounds for Local Density of Sphere Packings and the Kepler Conjecture1. Introduction; 2. Local Density Inequalities; 3. History; 4. Hales-Ferguson Partition Rule and Score Function; 5. Kepler Conjecture; 6. Concluding Remarks; Acknowledgments; Appendix A. Hales Score Function Formulas; Appendix B. References to the Hales Program Results; References; Part II: Proof of the Kepler Conjecture; Introduction to Part II; Guest Editors' Foreword; References; 3 Historical Overview of the Kepler Conjecture, by T. C. Hales; Contents; Historical Overview of the Kepler Conjecture; 1. Introduction
,
1.1. The Face-Centered Cubic Packing1.2. Early History, Hariot, and KeplerThe; 1.3. History; 1.4. The Literature; 1.4.1. Bounds.; 1.4.2. Classes of Packings.; 1.4.3. Other Convex Bodies.; 1.4.4. Strategies of Proof.; 2. Overview of the Proof; 2.1. Experiments with other Decompositions; 2.2. Contents of the Papers; 2.3. Complexity; 2.4. Computers; Acknowledgments; References; 4 A Formulation of the Kepler Conjecture, by T. C. Hales and S. P. Ferguson; Contents; A Formulation of the Kepler Conjecture; Introduction; 3. The Top-Level Structure of the Proof; 3.1. Statement of Theorems
,
3.2. Basic Concepts in the Proof3.3. Logical Skeleton of the Proof; 3.4. Proofs of the Central Claims; 4. Construction of the Q-System; 4.1. Description of the Q-system; 4.2. Geometric Considerations; 4.3. Incidence Relations; 4.4. Overlap of Simplices; 5. V-Cells; 6. Decomposition Stars; 6.1. Indexing Sets; 6.2. Cells Attached to Decomposition Stars; 6.3. Colored Spaces; 7. Scoring; 7.1. Definitions; 7.2. Negligibility; 7.3. Fcc-Compatibility; 7.4. Scores of Standard Clusters; 7.5. Scores of Simplices and Cones; 7.6. The Example of a Dodecahedron; References
,
5 Sphere Packings III. Extremal Cases, by T. C. Hales
,
Electronic reproduction; Available via World Wide Web
Additional Edition:
ISBN 9781461411284
Additional Edition:
Druckausg. The Kepler conjecture New York, NY [u.a.] : Springer, 2011 ISBN 9781461411284
Language:
English
Subjects:
Mathematics
Keywords:
Kepler-Vermutung
DOI:
10.1007/978-1-4614-1129-1
URL:
Volltext
(lizenzpflichtig)
Bookmarklink
