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Dense Sphere Packings
A Blueprint for Formal Proofs
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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, and Fejes Tóth's conjecture describing all packings of congruent balls in which every ball touches twelve others. 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.
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Cambridge University Press; September 2012
286 pages; ISBN 9781139579124
Read online, or download in EPUB or secure PDF format
286 pages; ISBN 9781139579124
Read online, or download in EPUB or secure PDF format
