TY  - BOOK
AU  - Hales,Thomas Callister
TI  - Dense sphere packings: a blueprint for formal proofs 
T2  - London Mathematical Society lecture note series
SN  - 9781139193894 (ebook)
AV  - QA166.7 .H35 2012
U1  - 511.6 22
PY  - 2012///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Sphere packings
KW  - Kepler's conjecture
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); 1. Close packing -- 2. Trigonometry -- 3. Volume -- 4. Hypermap -- 5. Fan -- 6. Packing -- -7. Local fan -- 8. Tame hypermap -- Appendix
N2  - 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
UR  - https://doi.org/10.1017/CBO9781139193894
ER  -