caa a22 4500 445836040 CHVBK 20180317145330.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00209-009-0644-2 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0644-2 Marchal Christian ONERA, General Scientific Direction, BP 72, Chatillon Cedex, France aut Study of the Kepler's conjecture: the problem of the closest packing [Elektronische Daten] [Christian Marchal] In the first and second parts the problem of the Kepler's conjecture is reduced from a problem with an infinite number of parameters to a problem with a finite number of parameters. In the third part is it is shown that the latter problem can be solved by a numerical verification using only a finite number of computations. However that finite number remains large, even if modern computers can do it. The method of analysis is classical: to each sphere of an arbitrary packing is associated a corresponding large enough "associated domain”, disjoint from all other similar domains, in the hope of obtaining an interesting upper limit of the space occupation coefficient. Many methods of association have been tried in the past and the new method presented in this study is complex, but very well adapted to the problem of interest. Springer-Verlag, 2009 Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 737-765 0025-5874 267:3-4<737 2011 267 209 https://doi.org/10.1007/s00209-009-0644-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0644-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Marchal Christian ONERA, General Scientific Direction, BP 72, Chatillon Cedex, France aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 737-765 0025-5874 267:3-4<737 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer