Dense Sphere Packings: A Blueprint for Formal Proofs (London Mathematical Society Lecture Note Series, Series Number 400)

The 400-year-old Kepler Conjecture Asserts That No Packing Of Congruent Balls In Three Dimensions Can Have A Density Exceeding The Familiar Pyramid-shaped Cannonball Arrangement. In This Book, A New Proof Of The Conjecture Is Presented That Makes It Accessible For The First Time To A Broad Mathematical Audience. The Book Also Presents Solutions To Other Previously Unresolved Conjectures In Discrete Geometry, Including The Strong Dodecahedral Conjecture On The Smallest Surface Area Of A Voronoi Cell In A Sphere Packing. This Book Is Also Currently Being Used As A Blueprint For A Large-scale Formal Proof Project, Which Aims To Check Every Logical Inference Of The Proof Of The Kepler Conjecture By Computer. This Is An Indispensable Resource For Those Who Want To Be Brought Up To Date With Research On The Kepler Conjecture--back Cover. 1. Close Packing -- 2. Trigonometry -- 3. Volume -- 4. Hypermap -- 5. Fan -- 6. Packing - -7. Local Fan -- 8. Tame Hypermap. Thomas C. Hales. Includes Bibliographical References (p. [262]-263) And Indexes. "The 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new proof of the conjecture is presented that makes it accessible for the first time to a broad mathematical audience. The book also presents solutions to other previously unresolved conjectures in discrete geometry, including the strong dodecahedral conjecture on the smallest surface area of a Voronoi cell in a sphere packing. This book is also currently being used as a blueprint for a large-scale formal proof project, which aims to check every logical inference of the proof of the Kepler conjecture by computer. This is an indispensable resource for those who want to be brought up to date with research on the Kepler conjecture"--Page [4] de la cob "The 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new proof of the conjecture is presented that makes it accessible for the first time to a broad mathematical audience. The book also presents solutions to other previously unresolved conjectures in discrete geometry, including the strong dodecahedral conjecture on the smallest surface area of a Voronoi cell in a sphere packing. This book is also currently being used as a blueprint for a large-scale formal proof project, which aims to check every logical inference of the proof of the Kepler conjecture by computer. This is an indispensable resource for those who want to be brought up to date with research on the Kepler conjecture"--P. [4] de la couv The 400-year-old Kepler conjecture about sphere packings is the oldest problem in discrete geometry. In this book, readers will learn about it through a proof that is much more accessible than the original proof of the theorem. Content: 1. Close packing 2. Trigonometry 3. Volume 4. Hypermap 5. Fan 6. Packing 7. Local fan 8. Tame hypermap 9. Further results. The definitive account of the recent computer solution of the oldest problem in discrete geometry