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Kepler conjecture
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==References== {{Reflist}} ===Publications=== *{{Citation | last1=Aste | first1=Tomaso | last2=Weaire | first2=Denis | title=The Pursuit of Perfect Packing|title-link=The Pursuit of Perfect Packing | publisher=IOP Publishing Ltd. | location=Bristol | isbn=978-0-7503-0648-5 | mr=1786410 | year=2000 | doi=10.1887/0750306483}} *{{citation | last1=Gauss | first1=Carl F. | author1-link=Carl Friedrich Gauss | date = 1831 | title = Untersuchungen über die Eigenschaften der positiven ternären quadratischen Formen von Ludwig August Seeber | url = https://babel.hathitrust.org/cgi/pt?id=mdp.39015064427944&seq=387 | journal = [[Göttingische gelehrte Anzeigen]] | issue = 108 | pages = 1065–1077}} *{{Citation | last1=Hales | first1=Thomas C. | title=Cannonballs and honeycombs | url=https://www.ams.org/notices/200004/ | mr=1745624 | year=2000 | journal=[[Notices of the American Mathematical Society]] | issn=0002-9920 | volume=47 | issue=4 | pages=440–449}} An elementary exposition of the proof of the Kepler conjecture. * {{Citation | doi=10.4007/annals.2005.162.1065 | last1=Hales | first1=Thomas C. | title=A proof of the Kepler conjecture | mr=2179728 | year=2005 | journal=[[Annals of Mathematics]] |series=Second Series | issn=0003-486X | volume=162 | issue=3 | pages=1065–1185| arxiv=math/9811078 }} *{{Citation | last1=Hales | first1=Thomas C. | title=Historical overview of the Kepler conjecture | doi=10.1007/s00454-005-1210-2 | mr=2229657 | year=2006 | journal=[[Discrete & Computational Geometry]] | issn=0179-5376 | volume=36 | issue=1 | pages=5–20| doi-access=free }} *{{Citation | last1=Hales | first1=Thomas C. | last2=Ferguson | first2=Samuel P. | s2cid=6529590 | title=A formulation of the Kepler conjecture | doi=10.1007/s00454-005-1211-1 | mr=2229658 | year=2006 | journal=[[Discrete & Computational Geometry]] | issn=0179-5376 | volume=36 | issue=1 | pages=21–69 | url=https://link.springer.com/content/pdf/10.1007%2Fs00454-005-1211-1.pdf| arxiv=math/9811078 }} *{{Citation | last1=Hales | first1=Thomas C. | last2=Ferguson | first2=Samuel P. | title=The Kepler Conjecture: The Hales-Ferguson Proof | publisher=Springer | location=New York | isbn=978-1-4614-1128-4 | year=2011}} *{{Citation | last1=Hales | first1=Thomas C. | title=Dense Sphere Packings: A Blueprint for Formal Proofs | journal=London Mathematical Society Lecture Note Series | volume=400 | publisher=Cambridge University Press | isbn=978-0-521-61770-3 | year=2012}} *{{Citation | last1=Henk | first1=Martin | last2=Ziegler | first2=Guenther | title=La congettura di Keplero|series=La matematica. Problemi e teoremi|volume=2|publisher=Einaudi|location=Torino|year=2008}} *{{Citation | doi=10.1142/S0129167X93000364 | last1=Hsiang | first1=Wu-Yi | title=On the sphere packing problem and the proof of Kepler's conjecture | mr=1245351 | year=1993 | journal=International Journal of Mathematics | issn=0129-167X | volume=4 | issue=5 | pages=739–831}} *{{Citation | last1=Hsiang | first1=Wu-Yi | s2cid=119641512 | title=A rejoinder to T. C. Hales's article: ''The status of the Kepler conjecture'' | doi=10.1007/BF03024716 | mr=1319992 | year=1995 | journal=[[The Mathematical Intelligencer]] | issn=0343-6993 | volume=17 | issue=1 | pages=35–42}} *{{Citation | last1=Hsiang | first1=Wu-Yi | title=Least action principle of crystal formation of dense packing type and Kepler's conjecture | publisher=World Scientific Publishing Co. Inc. | location=River Edge, NJ | series=Nankai Tracts in Mathematics | isbn=978-981-02-4670-9 | mr=1962807 | year=2001 | volume=3 | doi=10.1142/9789812384911}} *{{Citation | last1=Kepler | first1=Johannes | title=Strena seu de nive sexangula |trans-title=The six-cornered snowflake | url=http://www.thelatinlibrary.com/kepler/strena.html | year=1611| publisher=Paul Dry Books |mr=0927925|isbn=978-1-58988-053-5 |language=la}} **{{cite web |title=On the Six-Cornered Snowflake |website=Kepler's Discovery |url=http://www.keplersdiscovery.com/SixCornered.html |archive-url=https://web.archive.org/web/20071219221045/http://www.keplersdiscovery.com/SixCornered.html |archive-date=2007-12-19}} *{{Citation | last1=Hales | first1=Thomas C. | last2=MacLaughin | first2=Sean | title=The dodecahedral conjecture | journal=[[Journal of the American Mathematical Society]] | volume=23 | issue=2 | pages=299–344|year=2010 | doi=10.1090/S0894-0347-09-00647-X | arxiv=math.MG/9811079| bibcode=2010JAMS...23..299H }} *{{Citation | last1=Marchal | first1=Christian | s2cid=122088451 | title=Study of Kepler's conjecture: the problem of the closest packing | journal=[[Mathematische Zeitschrift]] | volume=267 | issue=3–4 | pages=737–765|year=2011 | doi=10.1007/s00209-009-0644-2}} *{{Citation | last1=Rogers | first1=C. A. | title=The packing of equal spheres | doi=10.1112/plms/s3-8.4.609 | mr=0102052 | year=1958 | journal=[[Proceedings of the London Mathematical Society]] |series=Third Series | issn=0024-6115 | volume=8 | issue=4 | pages=609–620}} *{{Citation | last1=Szpiro | first1=George G. | author-link= George Szpiro | title=Kepler's conjecture | publisher=[[John Wiley & Sons]] | location=New York | isbn=978-0-471-08601-7 | mr=2133723 | year=2003}} *{{Citation | last1=Fejes Tóth | first1=L. | author1-link=László Fejes Tóth | title=Lagerungen in der Ebene, auf der Kugel und im Raum | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXV |doi=10.1007/978-3-642-65234-9| mr=0057566 | year=1953| isbn=978-3-642-65235-6 }}
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