Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 6: Poster Session I

DY 6.12: Poster

Monday, March 22, 2010, 16:00–18:00, Poster B2

Investigation of the kissing number problem — •Sebiha Sahin, Andre Müller, Elmar Schömer, and Johannes J. Schneider — Center for Computational Research Methods in Natural Sciences, Johannes Gutenberg University of Mainz, Staudinger Weg 7, 55099 Mainz, Germany

We consider a problem which originates in its current form from a famous dispute between Sir Isaac Newton and the Scottish mathematician David Gregory in the year 1694. The question was how many equal spheres can touch a sphere of the same radius in their midst, without any overlaps. Newton correctly thought that the limit was 12; Gregory thought that a 13th could fit. The proof that Newton was correct was provided by Schütte and van der Waerden in 1953. Only for a few higher dimensions, the value of this kissing number is exactly known. Mostly, only lower and upper bounds to the kissing number can be estimated. We propose a heuristic optimization approach to this problem in higher dimensions and study the dynamics of the optimization process.