The Optimal Packing of Eight Points in the Real Projective Plane
EXPERIMENTAL MATHEMATICS(2022)
摘要
How can we arrange n lines through the origin in three-dimensional Euclidean space in a way that maximizes the minimum interior angle between pairs of lines? Conway, Hardin, and Sloane (1996) produced line packings for that they conjectured to be within numerical precision of optimal in this sense, but until now only the cases have been solved. In this paper, we resolve the case n = 8. Drawing inspiration from recent work on the Tammes problem, we enumerate contact graph candidates for an optimal configuration and eliminate those that violate various combinatorial and geometric necessary conditions. The contact graph of the putatively optimal numerical packing of Conway, Hardin, and Sloane is the only graph that survives, and we recover from this graph an exact expression for the minimum distance of eight optimally packed points in the real projective plane.
更多查看译文
关键词
Grassmannian manifolds, packing, frame theory
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络