Dense Sphere Packings

A Blueprint for Formal Proofs

Thomas Hales (University of Pittsburgh)

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English

Cambridge University Press
06 September 2012

Mathematics & Sciences; Combinatorics & graph theory; Applied mathematics

Series: London Mathematical Society Lecture Note Series

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.

By: Thomas Hales (University of Pittsburgh)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 400
Dimensions: Height: 228mm, Width: 152mm, Spine: 15mm
Weight: 420g
ISBN: 9780521617703
ISBN 10: 0521617707
Series: London Mathematical Society Lecture Note Series
Pages: 286
Publication Date: 06 September 2012
Audience: Professional and scholarly , Professional and scholarly , Undergraduate , Undergraduate
Format: Paperback
Publisher's Status: Active

1. Close packing; 2. Trigonometry; 3. Volume; 4. Hypermap; 5. Fan; 6. Packing; 7. Local fan; 8. Tame hypermap; 9. Further results.

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.

Reviews for Dense Sphere Packings: A Blueprint for Formal Proofs

'... 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 ... 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