论文标题
从理性台球中的圆形分区的整数序列
Integer Sequences from Circle Divisions in Rational Billiards
论文作者
论文摘要
我们研究理性的通告台球。通过查看每个反射点之后形成的轨迹，当圆圈的数量到区域中，我们为每次反射后的划分区域数量得出一个通用公式。这将导致整数分裂序列。限制特殊情况$ \ vartheta = \ frac {q} {2q+1} \ cdot2π$我们表明，每个反射$ n $之后的区域数与高斯的算术系列非常相关。
We study rational circular billiards. By viewing the trajectory formed after each reflection point to another inside the circle as the number of circle divisions into regions we derive a general formula for the number of division regions after each reflection. This will give rise to an integer division sequence. Restricting to the special cases $\vartheta =\frac{q}{2q+1}\cdot 2π$ we show that the number of regions after each reflection $n$ is beautifully related to Gauss 's arithmetic series.
