Dense Sphere Packings: A Blueprint for Formal Proofs: 400
Author(s): Thomas Hales (Author)
Publisher: Cambridge University Press
Publication Date: 6 Sept. 2012
Edition: Illustrated
Language: English
Print length: 286 pages
ISBN-10: 0521617707
ISBN-13: 9780521617703
Book Description
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.
Editorial Reviews
Review
‘… interesting and unusual book … beautifully written and is full of interesting historical notes. Moreover, each chapter is equipped with a very helpful summary, and many technical arguments are accompanied by a conceptual informal discussion. The book also features a detailed index and a nice bibliography. It is bound to become an indispensable resource for anyone wishing to study Kepler’s conjecture.’ Zentralblatt MATH
Book Description
The definitive account of the recent computer solution of the oldest problem in discrete geometry.
About the Author
Professor Thomas Hales is Andrew Mellon Professor at the University of Pittsburgh. He is best known for his solution to the 400-year-old Kepler conjecture and is also known for the proof of the honeycomb conjecture. He is currently helping to develop technology that would allow computers to do mathematical proofs. His honors include the Chauvenet Prize of the MAA, the R. E. Moore Prize, the Lester R. Ford Award of the MAA, the Robbins Prize of the AMS and the Fulkerson Prize of the Mathematical Programming Society.
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