标题： 正五边形在平面中的排列 显示英文标题

标题： Packings of Regular Pentagons in the Plane

摘要： 我们证明了欧几里得平面上每个正五边形的排列密度都小于0.9611。 我们的证明是计算机辅助的。 我们还提供了一个详细的策略来证明Kuperberg-Kuperberg猜想，该猜想断言平面中正五边形的最佳排列是一个双格子，由对齐的垂直列的向上指向的五边形和对齐的垂直列的向下指向的五边形交替组成。 该策略基于Delaunay三角形面积的估计。 我们的策略将Kuperberg猜想简化为最多涉及四个锐角Delaunay三角形的面积最小化问题。 显示英文摘要

摘要： We show that every packing of regular pentagons in the Euclidean plane has density less than 0.9611. Our proof is computer-assisted. We also give a detailed strategy for proving the Kuperberg-Kuperberg conjecture, which asserts that the optimal packing of regular pentagons in the plane is a double lattice, formed by aligned vertical columns of upward pointing pentagons alternating with aligned vertical columns of downward pointing pentagons. The strategy is based on estimates of the areas of Delaunay triangles. Our strategy reduces the Kuperberg conjecture to area minimization problems that involve at most four acute Delaunay triangles.