Mathematical billiards
Mathematical billiards
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数学台球
DOI：
10.2307/3618914
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
R. Shiflett
中科院分区：
文献类型：
--
作者：
Harris S. Shultz;R. Shiflett
从一个大小为m×n(其中m和n是整数)的长方形台球桌的角落以45度的角度射出一个球。它总是以45度的角度从一侧反弹，直到它落在角落的口袋里。它会永远落在角落里，还是会永远弹跳？它会弹几次？它会落在哪个角落的口袋里？你自己试试吧。例如，在图中所示的7×4表格中，球将反弹9次，然后落入左上角的口袋。这是一个众所周知的问题，但我们现在提出了一个比我们在其他地方看到的更简单的证明，证明了球总是落在角袋里，我们推导出了反弹次数的公式，并确定了最后一个袋。
A ball is shot at an angle of 45 degrees from the corner of a rectangular billiard table of size m × n (where m and n are integers). It always bounces off from a side at 45 degrees until it lands in a corner pocket. Will it always land in a corner or will it keep bouncing for ever? And how many times will it bounce? And which corner pocket will it land in? Try it for yourself. For example in the 7 × 4 table shown the ball will bounce 9 times and then fall into the top left-hand corner pocket. This is a well-known problem but we now present a simpler proof than we've seen elsewhere of the fact that the ball always ends up in a corner pocket, and we derive a formula for the number of bounces and we determine the finishing pocket.