论文标题
Segre定理在球形曲线上的离散类似物
A discrete analog of Segre's theorem on spherical curves
论文作者
论文摘要
我们证明了对于空间曲线的特定四个vertex定理的离散类似物。平滑的案例可以追溯到贝尼亚尼诺·塞格尔（Beniamino Segre）的工作，并指出，切线的封闭曲线没有自我交流，至少四个点其扭转消失了。我们的方法使用（封闭）多边形的离散切线指示的概念。然后，我们的定理指出，具有至少四个顶点的多边形，其离散的切线指示没有自身交流，至少可以承认四个扁平化，即，顶点的三个三联，以至于前面的顶点和以下顶点在平面的相同侧面跨越了这一三重序列。
We prove a discrete analog of a certain four-vertex theorem for space curves. The smooth case goes back to the work of Beniamino Segre and states that a closed and smooth curve whose tangent indicatrix has no self-intersections admits at least four points at which its torsion vanishes. Our approach uses the notion of discrete tangent indicatrix of a (closed) polygon. Our theorem then states that a polygon with at least four vertices and whose discrete tangent indicatrix has no self-intersections admits at least four flattenings, i.e., triples of vertices such that the preceding and following vertices are on the same side of the plane spanned by this triple.
