Dense Sphere Packings
A Blueprint for Formal Proofs
Seiten
2012
Cambridge University Press (Verlag)
978-0-521-61770-3 (ISBN)
Cambridge University Press (Verlag)
978-0-521-61770-3 (ISBN)
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.
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.
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.
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.
1. Close packing; 2. Trigonometry; 3. Volume; 4. Hypermap; 5. Fan; 6. Packing; 7. Local fan; 8. Tame hypermap; 9. Further results.
| Reihe/Serie | London Mathematical Society Lecture Note Series |
|---|---|
| Zusatzinfo | Worked examples or Exercises; Printed music items |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 228 mm |
| Gewicht | 420 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| Schlagworte | London Mathematical Society Lecture Note |
| ISBN-10 | 0-521-61770-7 / 0521617707 |
| ISBN-13 | 978-0-521-61770-3 / 9780521617703 |
| Zustand | Neuware |
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