Stepped Hyperplane and Extension of the Three Distance Theorem
Stepped Hyperplane and Extension of the Three Distance Theorem
复制标题
阶梯超平面与三距离定理的推广
DOI：
10.1515/9783110298208.81
复制
发表时间：
2013
影响因子：
1.6
通讯作者：
N. Chevallier
中科院分区：
文献类型：
--
作者：
N. Chevallier
三距离定理指出，给定一个实数θ和一个整数n，θ，2θ，…，nθ的小数部分将单位区间[0，1]分成n+1个最多有三个不同长度的区间。已经存在几个使用三角剖分而不是区间的二维扩展。我们给出了一个改进这些扩张的结果。这一结果应该接近最优。
The three distance Theorem states that given a real number θ and an integer n, the fractional parts of θ, 2θ, ..., nθ divide the unit interval [0, 1] into n + 1 intervals having three different lengths at most. Several two-dimensional extensions using triangulations instead of intervals already exist. We give a result improving these extensions. This result should be close to optimality.