| dc.description.abstract | The kissing number problem asks for the maximum number N of pairwise non-overlapping unit spheres that can simultaneously touch a central unit sphere in n-dimensional Euclidean space. The value is only known when n = 1, 2, 3, 4, 8, and 24.
This question seems simple. However, for hundreds of years, there are still few known answers. In 1694, there was a famous dispute occurred between Newton and Gregory. Newton believed that 12 was the correct answer to the kissing number in dimension 3. However, Gregory thought it was 13. In the end, Schütte and van der Waerden gave us the first proof of the kissing number in dimension 3, N = 12, in 1953.
During these hundreds of years, mathematicians had developed many ways to approximate the answer. There are some famous methods that are well known. For example, Odlyzko and Sloane′s linear programming solved the kissing number problem in dimension 8 and 24. Moreover, Musin′s extension of the linear programming solved the kissing number problem in dimension 4.
This study presents the linear programming method, and semidefinite programming method. We combine these methods to obtain a way to reproduce the result of the classical kissing number problem by a different method. We also offer the formula of four points semidefinite programming method to be the reference for latecomers. | en_US |