The Kepler Conjecture
The Hales-Ferguson Proof
(Sprache: Englisch)
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...
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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.
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.
Klappentext zu „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 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.
Inhaltsverzeichnis zu „The Kepler Conjecture “
Preface.- Part I, Introduction and Survey.- 1 The Kepler Conjecture and Its Proof, by J. C. Lagarias.- 2 Bounds for Local Density of Sphere Packings and the Kepler Conjecture, by J. C. Lagarias.- Part II, Proof of the Kepler Conjecture.- Guest Editor's Foreword.- 3 Historical Overview of the Kepler Conjecture, by T. C. Hales.- 4 A Formulation of the Kepler Conjecture, by T. C. Hales and S. P. Ferguson.- 5 Sphere Packings III. Extremal Cases, by T. C. Hales.- 6 Sphere Packings IV. Detailed Bounds, by T. C. Hales.- 7 Sphere Packings V. Pentahedral Prisms, by S. P. Ferguson.- 8 Sphere Packings VI. Tame Graphs and Linear Programs, by T. C. Hales.- Part III, A Revision to the Proof of the Kepler Conjecture.- 9 A Revision of the Proof of the Kepler Conjecture, by T. C. Hales, J. Harrison, S. McLaughlin, T. Nipkow, S. Obua, and R. Zumkeller.- Part IV, Initial Papers of the Hales Program.- 10 Sphere Packings I, by T. C. Hales.- 11 Sphere Packings II, by T. C. Hales.- Index of Symbols.- Index of Subjects.-
Autoren-Porträt von Thomas C. Hales, Samuel P. Ferguson
Thomas C. Hales, professor of mathematics at the University of Pittsburgh, began his efforts to solve the Kepler Conjecture in 1992. He is a pioneer in the use of computer proof techniques, and he continues to verify his proof of Kepler Conjecture through his work on the Flyspeck Project (F, P and K standing for Formal Proof of Kepler).Samuel P. Ferguson was a doctoral student of Hales'. In 1995, Ferguson began to work with Hales and made significant contributions to the proof of the Kepler Conjecture. He co-authored the paper detailing the historical context and formulation of the Conjecture. His doctoral thesis on Sphere Packings is also included.
Jeffrey C. Lagarias is a professor of mathematics at the University of Michigan, Ann Arbor. He was co-guest editor of the special issue of DCG that originally published the proofs.
Bibliographische Angaben
- Autoren: Thomas C. Hales , Samuel P. Ferguson
- 2012, 2011, XIV, 456 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Herausgegeben: Jeffrey C. Lagarias
- Verlag: Springer, Berlin
- ISBN-10: 1461411289
- ISBN-13: 9781461411284
- Erscheinungsdatum: 08.11.2011
Sprache:
Englisch
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