The Kepler Conjecture

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, published.

5 Sphere Packings III. Extremal Cases, by T.C. Hales.

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 t…