Dense sphere packings: a blueprint for formal proofs
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
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| Edition: | 1. publ. |
| Series: | London Mathematical Society lecture note series
400 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 271 S. graph. Darst. |
| ISBN: | 9780521617703 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Dense sphere packings
Autor: Hales, Thomas C
Jahr: 2012
Contents Preface page vii PART ONE OVERVIEW 1 Close Packing 3 1.1 History 3 1.2 Face-Centered Cubic 6 1.3 Hexagonal-Close Packing 10 1.4 Gauss 13 1.5 Thue 14 1.6 Dense Packings in a Nutshell 17 PART TWO FOUNDATIONS 23 Trigonometry 25 2.1 Background Knowledge 25 2.2 Trig Identities 27 2.3 Vector Geometry 33 2.4 Angle 39 2.5 Coordinates 51 2.6 Cycle 55 2.7 Chapter Summary 60 Volume 61 3.1 Background in Measure 61 3.2 Primitive Volume 63 3.3 Finiteness and Volume 70
vi Contents 4 Hypermap 72 4.1 Background on Permutations 73 4.2 Definitions 74 4.3 Walkup 78 4.4 Planarity 83 4.5 Path 86 4.6 Subquotient 91 4.7 Generation 95 5 Fan 112 5.1 Definitions 112 5.2 Topology 117 5.3 Planarity 121 5.4 Polyhedron 132 PART THREE THE KEPLER CONJECTURE 143 6 Packing 145 6.1 The Primitive State of Our Subject Revealed 145 6.2 Rogers Simplex 150 6.3 Cells 167 6.4 Clusters 180 6.5 Counting Spheres 185 7 Local Fan 194 7.1 Localization 194 7.2 Modification 203 7.3 Polarity 209 7.4 Main Estimate 212 8 Tame Hypermap 235 8.1 Definition 236 8.2 Contravening Hypermap 238 8.3 Contravention is Tame 243 8.4 Admissibility 248 8.5 Linear Programs 250 8.6 Strong Dodecahedral Theorem 252 Appendix A Credits 257 References 261 General index 264 Notation index 269
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| author | Hales, Thomas C. 1958- |
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| author_facet | Hales, Thomas C. 1958- |
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| discipline | Mathematik |
| edition | 1. publ. |
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| indexdate | 2024-07-10T00:17:32Z |
| institution | BVB |
| isbn | 9780521617703 |
| language | English |
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| publishDate | 2012 |
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| publisher | Cambridge Univ. Press |
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| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Hales, Thomas C. 1958- Verfasser (DE-588)137005822 aut Dense sphere packings a blueprint for formal proofs Thomas C. Hales 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2012 XIV, 271 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 400 Kugelpackung (DE-588)4165929-6 gnd rswk-swf Kugelpackung (DE-588)4165929-6 s DE-604 London Mathematical Society lecture note series 400 (DE-604)BV000000130 400 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024986050&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hales, Thomas C. 1958- Dense sphere packings a blueprint for formal proofs London Mathematical Society lecture note series Kugelpackung (DE-588)4165929-6 gnd |
| subject_GND | (DE-588)4165929-6 |
| title | Dense sphere packings a blueprint for formal proofs |
| title_auth | Dense sphere packings a blueprint for formal proofs |
| title_exact_search | Dense sphere packings a blueprint for formal proofs |
| title_full | Dense sphere packings a blueprint for formal proofs Thomas C. Hales |
| title_fullStr | Dense sphere packings a blueprint for formal proofs Thomas C. Hales |
| title_full_unstemmed | Dense sphere packings a blueprint for formal proofs Thomas C. Hales |
| title_short | Dense sphere packings |
| title_sort | dense sphere packings a blueprint for formal proofs |
| title_sub | a blueprint for formal proofs |
| topic | Kugelpackung (DE-588)4165929-6 gnd |
| topic_facet | Kugelpackung |
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