论文标题
封闭单位曲线的凸盖至少为0.1
A convex cover for closed unit curves has area at least 0.1
论文作者
论文摘要
我们改善了封闭单元曲线的最小凸盖区域的下限，从0.0975到0.1，这使其更接近当前最佳上限0.11023。我们通过考虑圆形凸面的最小面积，长度为1/2的线和矩形，侧面为0.1727 x 0.3273。通过使用几何方法和框搜索算法，我们证明了该区域至少为0.1。我们提供了非正式的数值证据，表明所获得的下限接近当前技术的极限，并且需要大幅新的想法才能显着超过0.10044。
We improve a lower bound for the smallest area of convex covers for closed unit curves from 0.0975 to 0.1, which makes it substantially closer to the current best upper bound 0.11023. We did this by considering the minimal area of convex hull of circle, line of length 1/2, and rectangle with side 0.1727 x 0.3273. By using geometric methods and the Box search algorithm, we proved that this area is at least 0.1. We give informal numerical evidence that the obtained lower bound is close to the limit of current techniques, and substantially new idea is required to go significantly beyond 0.10044.
