Dense Sphere Packings
DOWNLOAD eBooks
Download Dense Sphere Packings PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Dense Sphere Packings book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Dense Sphere Packings
DOWNLOAD eBooks
Author : Thomas Callister Hales
language : en
Publisher: Cambridge University Press
Release Date : 2012-09-06
Dense Sphere Packings written by Thomas Callister Hales and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-06 with Mathematics categories.
The definitive account of the recent computer solution of the oldest problem in discrete geometry.
Dense Sphere Packings
DOWNLOAD eBooks
Author : Thomas Callister Hales
language : en
Publisher:
Release Date : 2014-05-14
Dense Sphere Packings written by Thomas Callister Hales and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
The definitive account of the recent computer solution of the oldest problem in discrete geometry.
Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler S Conjecture
DOWNLOAD eBooks
Author : Wu Yi Hsiang
language : en
Publisher: World Scientific
Release Date : 2001
Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler S Conjecture written by Wu Yi Hsiang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal ?known density? of B/û18. In 1611, Johannes Kepler had already ?conjectured? that B/û18 should be the optimal ?density? of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that B/û18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry.
Calculations Of Hard Sphere Packings In Large Cylinders
DOWNLOAD eBooks
Author : Brian E. Clancy
language : en
Publisher:
Release Date : 1966
Calculations Of Hard Sphere Packings In Large Cylinders written by Brian E. Clancy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.
Sphere Packings And The Concept Of Density
DOWNLOAD eBooks
Author : Jörg M. Wills
language : en
Publisher:
Release Date : 1995
Sphere Packings And The Concept Of Density written by Jörg M. Wills and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Sphere Packings Lattices And Groups
DOWNLOAD eBooks
Author : J.H. Conway
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Sphere Packings Lattices And Groups written by J.H. Conway and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The second edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics. Results as of 1992 have been added to the text, and the extensive bibliography - itself a contribution to the field - is supplemented with approximately 450 new entries.
On The Density Of Sphere Packings In E
DOWNLOAD eBooks
Author : Wu Yi Hsiang
language : en
Publisher:
Release Date : 1991
On The Density Of Sphere Packings In E written by Wu Yi Hsiang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Combinatorial packing and covering categories.
Sphere Packings
DOWNLOAD eBooks
Author : Chuanming Zong
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-08-19
Sphere Packings written by Chuanming Zong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-19 with Mathematics categories.
Sphere packings is one of the most fascinating and challenging subjects in mathematics. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with other subjects found. This book gives a full account of this fascinating subject, especially its local aspects, discrete aspects, and its proof methods. The book includes both classical and contemporary results and provides a full treatment of the subject.
The Kepler Conjecture
DOWNLOAD eBooks
Author : Jeffrey C. Lagarias
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-09
The Kepler Conjecture written by Jeffrey C. Lagarias and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-09 with Mathematics categories.
The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of three-dimensional Euclidean space by equal spheres is attained by the “cannonball" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use of computers. This book centers around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, published in 2006 in a special issue of Discrete & Computational Geometry. Further supporting material is also presented: a follow-up paper of Hales et al (2010) revising the proof, and describing progress towards a formal proof of the Kepler conjecture. For historical reasons, this book also includes two early papers of Hales that indicate his original approach to the conjecture. The editor's two introductory chapters situate the conjecture in a broader historical and mathematical context. These chapters provide a valuable perspective and are a key feature of this work.
Lectures On Sphere Arrangements The Discrete Geometric Side
DOWNLOAD eBooks
Author : Károly Bezdek
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-04
Lectures On Sphere Arrangements The Discrete Geometric Side written by Károly Bezdek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-04 with Mathematics categories.
This monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains more than 40 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course. The core part of this book is based on three lectures given by the author at the Fields Institute during the thematic program on “Discrete Geometry and Applications” and contains four core topics. The first two topics surround active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres, is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic of this book can be found under the sections on ball-polyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the above-mentioned major topics and it is also connected to some other important research areas as the one on coverings by planks (with close ties to geometric analysis). This fourth core topic is discussed under covering balls by cylinders.