Dense sphere packings: a blueprint for formal proofs
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 mathemati...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2012
|
| Series: | London Mathematical Society lecture note series
400 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xiv, 271 pages) |
| ISBN: | 9781139193894 |
| DOI: | 10.1017/CBO9781139193894 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043942337 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2012 |||| o||u| ||||||eng d | ||
| 020 | |a 9781139193894 |c Online |9 978-1-139-19389-4 | ||
| 024 | 7 | |a 10.1017/CBO9781139193894 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9781139193894 | ||
| 035 | |a (OCoLC)847029281 | ||
| 035 | |a (DE-599)BVBBV043942337 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 511.6 |2 22 | |
| 084 | |a SK 170 |0 (DE-625)143221: |2 rvk | ||
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a SK 380 |0 (DE-625)143235: |2 rvk | ||
| 100 | 1 | |a Hales, Thomas Callister |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Dense sphere packings |b a blueprint for formal proofs |c Thomas C. Hales |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2012 | |
| 300 | |a 1 online resource (xiv, 271 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a London Mathematical Society lecture note series |v 400 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a 1. Close packing -- 2. Trigonometry -- 3. Volume -- 4. Hypermap -- 5. Fan -- 6. Packing -- -7. Local fan -- 8. Tame hypermap -- Appendix | |
| 520 | |a 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 | ||
| 650 | 4 | |a Sphere packings | |
| 650 | 4 | |a Kepler's conjecture | |
| 650 | 0 | 7 | |a Kugelpackung |0 (DE-588)4165929-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kugelpackung |0 (DE-588)4165929-6 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-61770-3 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9781139193894 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029351307 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1017/CBO9781139193894 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9781139193894 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Record in the Search Index
| _version_ | 1804176885011185664 |
|---|---|
| any_adam_object | |
| author | Hales, Thomas Callister |
| author_facet | Hales, Thomas Callister |
| author_role | aut |
| author_sort | Hales, Thomas Callister |
| author_variant | t c h tc tch |
| building | Verbundindex |
| bvnumber | BV043942337 |
| classification_rvk | SK 170 SK 180 SK 380 |
| collection | ZDB-20-CBO |
| contents | 1. Close packing -- 2. Trigonometry -- 3. Volume -- 4. Hypermap -- 5. Fan -- 6. Packing -- -7. Local fan -- 8. Tame hypermap -- Appendix |
| ctrlnum | (ZDB-20-CBO)CR9781139193894 (OCoLC)847029281 (DE-599)BVBBV043942337 |
| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139193894 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02901nmm a2200505zcb4500</leader><controlfield tag="001">BV043942337</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2012 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139193894</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-139-19389-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9781139193894</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9781139193894</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)847029281</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043942337</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.6</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 170</subfield><subfield code="0">(DE-625)143221:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 380</subfield><subfield code="0">(DE-625)143235:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hales, Thomas Callister</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Dense sphere packings</subfield><subfield code="b">a blueprint for formal proofs</subfield><subfield code="c">Thomas C. Hales</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xiv, 271 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">London Mathematical Society lecture note series</subfield><subfield code="v">400</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">1. Close packing -- 2. Trigonometry -- 3. Volume -- 4. Hypermap -- 5. Fan -- 6. Packing -- -7. Local fan -- 8. Tame hypermap -- Appendix</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sphere packings</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Kepler's conjecture</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kugelpackung</subfield><subfield code="0">(DE-588)4165929-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kugelpackung</subfield><subfield code="0">(DE-588)4165929-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-61770-3</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9781139193894</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029351307</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781139193894</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781139193894</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043942337 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9781139193894 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351307 |
| oclc_num | 847029281 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xiv, 271 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Hales, Thomas Callister Verfasser aut Dense sphere packings a blueprint for formal proofs Thomas C. Hales Cambridge Cambridge University Press 2012 1 online resource (xiv, 271 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 400 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1. Close packing -- 2. Trigonometry -- 3. Volume -- 4. Hypermap -- 5. Fan -- 6. Packing -- -7. Local fan -- 8. Tame hypermap -- Appendix 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 Sphere packings Kepler's conjecture Kugelpackung (DE-588)4165929-6 gnd rswk-swf Kugelpackung (DE-588)4165929-6 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-61770-3 https://doi.org/10.1017/CBO9781139193894 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hales, Thomas Callister Dense sphere packings a blueprint for formal proofs 1. Close packing -- 2. Trigonometry -- 3. Volume -- 4. Hypermap -- 5. Fan -- 6. Packing -- -7. Local fan -- 8. Tame hypermap -- Appendix Sphere packings Kepler's conjecture 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 | Sphere packings Kepler's conjecture Kugelpackung (DE-588)4165929-6 gnd |
| topic_facet | Sphere packings Kepler's conjecture Kugelpackung |
| url | https://doi.org/10.1017/CBO9781139193894 |
| work_keys_str_mv | AT halesthomascallister densespherepackingsablueprintforformalproofs |