The Kepler Conjecture

The Hales-Ferguson Proof

Editors: Lagarias, Jeffrey C. (Ed.)

  • Complete solution of a four hundred year old geometry problem
  • A fundamental achievement in discrete geometry and mathematical physics
  • Provides history and summary of approaches to the problem
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About this book

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 in 2006 in a special issue of Discrete & Computational Geometry. Further supporting material is also presented: a follow-up paper of Hales et al (2010) revising the proof, and describing progress towards a formal proof of the Kepler conjecture. For historical reasons, this book also includes two early papers of Hales that indicate his original approach to the conjecture.

The editor's two introductory chapters situate the conjecture in a broader historical and mathematical context. These chapters provide a valuable perspective and are a key feature of this work.

Thomas C. Hales, Mellon Professor of Mathematics at the University of Pittsburgh, began his efforts to solve the Kepler conjecture before 1992. He is a pioneer in the use of computer proof techniques, and he continues work on a formal proof of the Kepler conjecture as the aim of the Flyspeck Project (F, P and K standing for Formal Proof of Kepler).

Samuel P. Ferguson completed his doctorate in 1997 under the direction of Hales at the University of Michigan. In 1995, Ferguson began to work with Hales and made significant contributions to the proof of the Kepler conjecture. His doctoral work established one crucial case of the proof, which appeared as a singly authored paper in the detailed proof.

Jeffrey C. Lagarias, Professor of Mathematics at the University of Michigan, Ann Arbor, was a co-guest editor, with Gábor Fejes-Tóth, of the special issue of Discrete & Computational Geometry that originally published the proof.

About the authors

Thomas C. Hales, Mellon Professor of Mathematics at the University of Pittsburgh, began his efforts to solve the Kepler Conjecture before 1992. He is a pioneer in the use of computer proof techniques, and he continues work on a formal proof of the Kepler Conjecture as the aim of the Flyspeck Project (F, P and K standing for Formal Proof of Kepler).

Samuel P. Ferguson completed his doctorate in 1997 under the direction of Hales at the University of Michigan. In 1995, Ferguson began to work with Hales and made significant contributions to the proof of the Kepler Conjecture. His doctoral work established one crucial case of the proof, which appeared as a singly authored paper in the detailed proof.

Jeffrey C. Lagarias, Professor of Mathematics at the University of Michigan, Ann Arbor, was a co-guest editor, with Gábor Fejes-Tóth, of the special issue of Discrete & Computational Geometry that originally published the proof.

Table of contents (12 chapters)

  • The Kepler Conjecture and Its Proof

    Lagarias, Jeffrey C.

    Pages 3-26

  • Bounds for Local Density of Sphere Packings and the Kepler Conjecture

    Lagarias, J. C.

    Pages 27-57

  • Historical Overview of the Kepler Conjecture

    Hales, Thomas C.

    Pages 65-82

  • A Formulation of the Kepler Conjecture

    Hales, Thomas C. (et al.)

    Pages 83-133

  • Sphere Packings, III. Extremal Cases

    Hales, Thomas C.

    Pages 135-176

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4614-1129-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-1-4614-1128-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Kepler Conjecture
Book Subtitle
The Hales-Ferguson Proof
Editors
  • Jeffrey C. Lagarias
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-1129-1
DOI
10.1007/978-1-4614-1129-1
Softcover ISBN
978-1-4614-1128-4
Edition Number
1
Number of Pages
XIV, 456
Number of Illustrations and Tables
82 b/w illustrations, 11 illustrations in colour
Topics