The Kepler Conjecture

The Kepler Conjecture was one of geometry s oldest unsolved problems. Formulated in 1611 by Johannes Kepler, the Conjecture states that the densest packing of a three-dimensional Euclidean space by equal spheres is attained by "cannonball" packing. The Conjecture was finally proven in 1998 with the use of computers by Thomas Hales, with help from Samuel P. Ferguson. This book is a landmark publication that bridges computer techniques with human effort in one of the earliest proofs by "exhaustion."The book is an expanded version of six papers published in a special issue of the field's foremost journal, Discrete & Computational Geometry. It also includes the original papers, which detail the proof and give a historical overview of the Conjecture. There are three additional appendices by Hales that outline extensive revisions to the proof and describe his original approach to the problem. Two new introductory chapters by the editor situate the Conjecture in a broader historical and mathematical context and a generalization of the Conjecture to more than three dimensions.