强十三球问题
The strong thirteen spheres problem
摘要：
13个球体问题是问在三维空间中13个大小相等的不重叠的球体是否可以接触到另一个大小相同的球体。这个问题是艾萨克·牛顿和大卫·格雷戈里在1694年进行的著名讨论的主题。这个问题是解决了舒特和范德瓦尔登只有在1953年。这个问题的一个自然扩张是强13球问题（或13点的Tammes问题），它要求找到一个安排和最大半径的13个相等大小的非重叠的领域接触单位球。本文给出了这一几何上长期未解决的问题的一种解法。我们的计算机辅助证明是基于所谓的不可约图的枚举。
英文摘要：
The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
