论文标题
最短的闭合曲线检查球体
Shortest closed curve to inspect a sphere
论文作者
论文摘要
我们表明，在Euclidean 3空间中，任何位于单位球体外部并包含凸面内的球体的闭合曲线至少为4π$。仅当曲线由$ 4 $的长度$π$组成时，平等才能保持平等，该曲线以棒球接缝的形状排列，这是V. A. Zalgaller在1996年的猜想。
We show that in Euclidean 3-space any closed curve which lies outside the unit sphere and contains the sphere within its convex hull has length at least $4π$. Equality holds only when the curve is composed of $4$ semicircles of length $π$, arranged in the shape of a baseball seam, as conjectured by V. A. Zalgaller in 1996.
