论文标题
台球中的切割序列和斯特里亚人序列
Cutting sequence and Sturmian sequence in billiard
论文作者
论文摘要
台球的胜利规则是将台球舞台上的台球舞到指定的孔中。我们尝试研究台球球的轨迹，以便我们可以预测球的方向。对于有理斜率，我们通过设置正方形圆环来剪切序列。我们使用剪切和翻转简化了切割序列，并获得了轨迹斜率和切割序列之间的转换。对于非理性斜率，我们查看Sturmian序列的某些特性，这些特性有助于我们区分切割序列和Sturmian序列。总之，对于不同的斜率，我们使用不同的序列进行研究。
The winning rule of billiards is to drive the billiard ball on the table into the designated holes. We try to study the trajectory of the billiard ball, so that we can predict the direction of the ball. For rational slopes, we got cutting sequence by setting up the square torus. We simplified cutting sequence using shearing and flipping and we obtain the transformation between trajectory slope and cutting sequence. For irrational slopes, we look at some properties of Sturmian sequence, which help us distinguish between cutting sequence and Sturmian sequence. In conclusion, in the case of different slopes, we use different sequences to do research.
