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?

Author: John Conway

Publisher: Springer Science & Business Media

ISBN: 9781475765687

Category: Mathematics

Page: 706

View: 149

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.

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?

Author: J.H. Conway

Publisher: Springer Science & Business Media

ISBN: 9781475722499

Category: Mathematics

Page: 682

View: 922

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.

This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local ...

Author: Jacques Martinet

Publisher: Springer Science & Business Media

ISBN: 9783662051672

Category: Mathematics

Page: 526

View: 872

Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3. This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property. Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290. Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices.

These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews between 1984 and 1996. This is the third such set of volumes in number theory. The first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.

In 1988 Conway and American mathematician Neil J . H . Sloane coauthored the
book Sphere Packing , Lattices , and Groups , which presented a survey of recent
research results in combinatorics , the study of counting techniques .

Literatur [ 1 ] J . H . Conway , N . J . A . Sloane , Sphere Packings , Lattices and Groups , 3rd edit . Springer , Berlin 1998 . [ 2 ] L . Fejes Toth , Lagerungen in der
Ebene , auf der Kugel und im Raum , Springer , Berlin 1953 . [ 3 ] P . M . Gruber ,
C ...

of points on ) is the MEASURE of the SET E i lattice which is A004009). the theta
series of the E8 (Sloane's Le Cam's Identity Let Sn be the sum of n random ... §
4.11, Ch. 12, and Chs. 23Á/6 in Sphere Packings, Lattices, and Groups, 2nd ed.

Author: Eric W. Weisstein

Publisher: CRC Press

ISBN: 9781420035223

Category: Mathematics

Page: 3252

View: 899

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

[ 3 ] A . Bezdek and W . Kuperberg , Packing Euclidean space with congruent
cylinders and with congruent ellipsoids , in ... [ 16 ] J . H . Conway and N . J . A .
Sloane , Sphere Packings , Lattices and Groups , Springer - Verlag , NY , 3rd
edition ...

[ Ba ] Bargmann , V. , Irreducible unitary representations of the Lorentz group ,
Ann . of Math . 48 ( 1947 ) , 568-640 . [ Bu ] Bump , D. ... [ CS ] Conway , J. H. ,
and N.J.A. Sloane , Sphere Packings , Lattices , and Groups . Springer - Verlag ,
1988 .

Author: Royal Society (Great Britain)Publish On: 1989

odd - dimensional lattices of determinant 2 ( for a list of these lattices see part I or
Conway & Sloane ( 1988a ) , tables 16 . 7 , 15 . 8 ) . E , lattice ... Conway , J . H . &
Sloane , N . J . A . 1988a Sphere packings , lattices and groups . New York ...

This approach allows a better understanding of the sphere hardening and the
use of lattice codes to achieve the ... 893 - 899 [ 13 ] J . H . Conway and N . J . A .
Sloane , Sphere packings , lattices and groups , NY : Springer , 1988 ( 14 ) M ...

Each rigid sphere packing has the density equal to the maximal possible density
of a lattice sphere packing in a three ... space . a net REFERENCES [ 1 ] J . H .
Conway and N . J . A . Sloane , Sphere Packings , Lattices and Groups , Vol .

is less elegant and we come to families of lattices with a 5 2 . 30 . . . and families
of non - lattice packings with a $ 1 . 31 . . . . References ( 1 ) Conway J . H . , N . J .
A . Sloane , Sphere Packings , Lattices and Groups , 2nd edition .

Author: Ruud Pellikaan

Publisher: De Gruyter

ISBN: UOM:39015037428292

Category: Computers

Page: 288

View: 471

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Cassels , J. W. S. An Introduction to the Geometry of Numbers , Springer - Verlag
, N. Y. , second printing , 1971 Conway , J. H. and Sloane , N. J. A. Sphere Packings , Lattices and Groups , Springer - Verlag , N. Y. , 1987 Gradshteyn , I.S.
and ...

Conway , J . H . & Sloane , N . J . A . 1999 Sphere packings , lattices and groups ,
3rd edn . New York , NY : Springer . Conway , J . H . , Hardin , R . H . & Sloane , N
. J . A . 1996 Packing lines , planes , etc . : packings in Grassmannian spaces .

The lattice A ' is invariant under G2 and isometric to the lattice of roots of type Es .
This lattice can be constructed by means of ... J . H . Conway and N . J . A .
Sloane , Sphere packings , lattices and groups , Springer - Verlag , Berlin , 1988 .

This book is being published in conjunction with the 50th anniversary of the Canadian Mathematical Society and it is a collection of 26 papers written by Dr. Coxeter.

Author: F. Arthur Sherk

Publisher: John Wiley & Sons

ISBN: 0471010030

Category: Mathematics

Page: 472

View: 151

H.S.M. Coxeter is one of the world's best-known mathematicians who wrote several papers and books on geometry, algebra and topology, and finite mathematics. This book is being published in conjunction with the 50th anniversary of the Canadian Mathematical Society and it is a collection of 26 papers written by Dr. Coxeter.

This classic text is devoted to describing crystal structures, especially periodic structures, and their symmetries. Updated material prepared by author enhances presentation, which can serve as text or reference. 1996 edition.

Author: Michael O'Keeffe

Publisher: Courier Dover Publications

ISBN: 9780486836546

Category: Science

Page: 480

View: 982

This classic text is devoted to describing crystal structures, especially periodic structures, and their symmetries. Updated material prepared by author enhances presentation, which can serve as text or reference. 1996 edition.