'Kissing' in Higher Dimensions

CWI - Christine Bachoc, Université Bordeaux, and Frank Vallentin, CWI, have found new upper bounds for 'kissing' in higher dimensions. In geometry the kissing number is the maximum number of non-overlapping unit balls that can simultaneously touch a central unit ball. In two dimensions the kissing number is six. This can be seen when euro coins are grouped around one central euro coin (see picture). The kissing number is only known for the dimensions 1, 2, 3, 4, 8 and 24. For the dimensions 5, 6, 7, 9 and 10 Bachoc and Vallentin now found sharper upper bounds. The kissing problem has a rich history. In 1694 Isaac Newton and David Gregory had a famous discussion about the kissing number in three dimensions. Gregory thought thirteen balls could fit while Newton believed the limit was twelve. Only in 1953, Schütte and Van der Waerden proved Newton right.

An article explaining the results is available at http://arxiv.org/abs/math.MG/0608426