Verfügbarkeit: Sphere Packings, Lattices and Groups | Technische Universität München

Sphere Packings, Lattices and Groups:

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Bibliographische Detailangaben
Beteilige Person:	Conway, John Horton 1937-2020 (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	Englisch
Veröffentlicht:	New York, NY Springer New York 1988
Schriftenreihe:	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 290
Schlagwörter:	Mathematics Chemistry / Mathematics Group theory Combinatorics Number theory Engineering Group Theory and Generalizations Number Theory Theoretical, Mathematical and Computational Physics Math. Applications in Chemistry Computational Intelligence Chemie Ingenieurwissenschaften Mathematik Gittertheorie Überdeckung > Mathematik Klassifikation Packungsproblem Kugelpackung Quadratische Form Kombinatorik Gitter > Mathematik
Links:	https://doi.org/10.1007/978-1-4757-2016-7
Beschreibung:	The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, . . . . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for the least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion (or data compression), which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices. When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A , which are unexpectedly good and very 24 symmetrical packings, and have a number of remarkable and mysterious properties, not all of which are completely understood even today
Umfang:	1 Online-Ressource (XXVII, 665 p)
ISBN:	9781475720167 9781475720181
ISSN:	0072-7830
DOI:	10.1007/978-1-4757-2016-7

Internformat

MARC


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500			\|a The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, . . . . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for the least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion (or data compression), which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices. When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A , which are unexpectedly good and very 24 symmetrical packings, and have a number of remarkable and mysterious properties, not all of which are completely understood even today
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id	DE-604.BV042421305
illustrated	Not Illustrated
indexdate	2024-12-20T17:10:44Z
institution	BVB
isbn	9781475720167 9781475720181
issn	0072-7830
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-027856722
oclc_num	864045759
open_access_boolean
owner	DE-384 DE-703 DE-91 DE-BY-TUM DE-634
owner_facet	DE-384 DE-703 DE-91 DE-BY-TUM DE-634
physical	1 Online-Ressource (XXVII, 665 p)
psigel	ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive
publishDate	1988
publishDateSearch	1988
publishDateSort	1988
publisher	Springer New York
record_format	marc
series2	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
spellingShingle	Conway, John Horton 1937-2020 Sphere Packings, Lattices and Groups Mathematics Chemistry / Mathematics Group theory Combinatorics Number theory Engineering Group Theory and Generalizations Number Theory Theoretical, Mathematical and Computational Physics Math. Applications in Chemistry Computational Intelligence Chemie Ingenieurwissenschaften Mathematik Gittertheorie (DE-588)4157394-8 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Klassifikation (DE-588)4030958-7 gnd Packungsproblem (DE-588)4173057-4 gnd Kugelpackung (DE-588)4165929-6 gnd Quadratische Form (DE-588)4128297-8 gnd Kombinatorik (DE-588)4031824-2 gnd Gitter Mathematik (DE-588)4157375-4 gnd
subject_GND	(DE-588)4157394-8 (DE-588)4186551-0 (DE-588)4030958-7 (DE-588)4173057-4 (DE-588)4165929-6 (DE-588)4128297-8 (DE-588)4031824-2 (DE-588)4157375-4
title	Sphere Packings, Lattices and Groups
title_auth	Sphere Packings, Lattices and Groups
title_exact_search	Sphere Packings, Lattices and Groups
title_full	Sphere Packings, Lattices and Groups by J. H. Conway, N. J. A. Sloane
title_fullStr	Sphere Packings, Lattices and Groups by J. H. Conway, N. J. A. Sloane
title_full_unstemmed	Sphere Packings, Lattices and Groups by J. H. Conway, N. J. A. Sloane
title_short	Sphere Packings, Lattices and Groups
title_sort	sphere packings lattices and groups
topic	Mathematics Chemistry / Mathematics Group theory Combinatorics Number theory Engineering Group Theory and Generalizations Number Theory Theoretical, Mathematical and Computational Physics Math. Applications in Chemistry Computational Intelligence Chemie Ingenieurwissenschaften Mathematik Gittertheorie (DE-588)4157394-8 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Klassifikation (DE-588)4030958-7 gnd Packungsproblem (DE-588)4173057-4 gnd Kugelpackung (DE-588)4165929-6 gnd Quadratische Form (DE-588)4128297-8 gnd Kombinatorik (DE-588)4031824-2 gnd Gitter Mathematik (DE-588)4157375-4 gnd
topic_facet	Mathematics Chemistry / Mathematics Group theory Combinatorics Number theory Engineering Group Theory and Generalizations Number Theory Theoretical, Mathematical and Computational Physics Math. Applications in Chemistry Computational Intelligence Chemie Ingenieurwissenschaften Mathematik Gittertheorie Überdeckung Mathematik Klassifikation Packungsproblem Kugelpackung Quadratische Form Kombinatorik Gitter Mathematik
url	https://doi.org/10.1007/978-1-4757-2016-7
work_keys_str_mv	AT conwayjohnhorton spherepackingslatticesandgroups AT sloaneneilja spherepackingslatticesandgroups

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