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Sphere Packings, Lattices and Groups

Sphere Packings, Lattices and Groups
Author: J.H. Conway
Publisher: Springer Science & Business Media
Total Pages: 724
Release: 2013-03-09
Genre: Mathematics
ISBN: 1475722494

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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.


Dense Sphere Packings

Dense Sphere Packings
Author: Thomas Callister Hales
Publisher: Cambridge University Press
Total Pages: 286
Release: 2012-09-06
Genre: Mathematics
ISBN: 0521617707

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The definitive account of the recent computer solution of the oldest problem in discrete geometry.


Sphere Packings

Sphere Packings
Author: Chuanming Zong
Publisher: Springer Science & Business Media
Total Pages: 245
Release: 2008-01-20
Genre: Mathematics
ISBN: 0387227806

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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.


Sphere Packings, Lattices and Groups

Sphere Packings, Lattices and Groups
Author: John Conway
Publisher: Springer Science & Business Media
Total Pages: 778
Release: 2013-06-29
Genre: Mathematics
ISBN: 1475765681

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The third edition of this 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 examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.


From Error-Correcting Codes Through Sphere Packings to Simple Groups

From Error-Correcting Codes Through Sphere Packings to Simple Groups
Author: Thomas M. Thompson
Publisher: American Mathematical Soc.
Total Pages: 228
Release: 1983-12-31
Genre:
ISBN: 1470454602

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This book traces a remarkable path of mathematical connections through seemingly disparate topics. Frustrations with a 1940's electro-mechanical computer at a premier research laboratory begin this story. Subsequent mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels lead to discoveries of extremely efficient lattice packings of equal-radius balls, especially in 24-dimensional space. In turn, this highly symmetric lattice, with each point neighboring exactly 196,560 other points, suggested the possible presence of new simple groups as groups of symmetries. Indeed, new groups were found and are now part of the "Enormous Theorem"—the classification of all simple groups whose entire proof runs some 10,000+ pages—and these connections, along with the fascinating history and the proof of the simplicity of one of those "sporatic" simple groups, are presented at an undergraduate mathematical level.


The Kepler Conjecture

The Kepler Conjecture
Author: Jeffrey C. Lagarias
Publisher: Springer Science & Business Media
Total Pages: 456
Release: 2011-11-09
Genre: Mathematics
ISBN: 1461411297

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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.


Dense Sphere Packings

Dense Sphere Packings
Author: Thomas Hales
Publisher: Cambridge University Press
Total Pages: 286
Release: 2012-09-06
Genre: Mathematics
ISBN: 113957647X

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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. 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.


Pedagogy and Content in Middle and High School Mathematics

Pedagogy and Content in Middle and High School Mathematics
Author: G. Donald Allen
Publisher:
Total Pages: 310
Release: 2017-10-13
Genre: Mathematics
ISBN: 9789463511360

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The book provides an accumulation of articles, included in Focus on Mathematics Pedagogy and Content, a newsletter for teachers, published by Texas A&M University. Each article presents a discussion of a middle or high school mathematics topic. Many of the articles are written by professors at Texas A&M University. The book is broken into three parts, with the first part focusing on content and pedagogy, related to the NCTM content strands of Number, Algebra, Geometry, Measurement, and Statistics and Probability. Articles include an in-depth presentation of mathematical content, as well as suggested instructional strategies. Thus, the integration of content knowledge and pedagogical knowledge is emphasized. The second and third parts apply to assessments, mathematical games, teaching tips, and technological applications. While other pedagogical reference books may provide an in-depth look at how to teach a topic, this book includes articles that also explain a topic, in great length. Thus, teachers may develop content knowledge first and then re-read each article, in order to learn appropriate instructional strategies to use. Many articles include technological applications, which are interspersed throughout the book. In addition, a special section, which includes helpful information, available tools, training sessions, and other references, for using technology in mathematics, is also presented.


Sphere Packings, V.

Sphere Packings, V.
Author: Samuel L. P. Ferguson
Publisher:
Total Pages: 208
Release: 1997
Genre: Sphere packings
ISBN:

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