Collisions, or Reflections and Rotations, Leading to the Digits of π  

作　　者：Franç ois Dubeau François Dubeau(Département de Mathématiques, Université de Sherbrooke, Sherbrooke (QC), Canada)

机构地区：[1]Département de Mathématiques, Université de Sherbrooke, Sherbrooke (QC), Canada

出　　处：《Applied Mathematics》2022年第9期705-732,共28页应用数学（英文）

摘　　要：We analyze a problem of elastic collisions between elements of a system composed of two balls and a wall. Thanks to a change of variables, the problem is reduced to a sequence of reflections and rotations. Moreover, the total number of collisions is easily found. For specific ratios of ball weights, the number of collisions is related to the first successive digits of π.We analyze a problem of elastic collisions between elements of a system composed of two balls and a wall. Thanks to a change of variables, the problem is reduced to a sequence of reflections and rotations. Moreover, the total number of collisions is easily found. For specific ratios of ball weights, the number of collisions is related to the first successive digits of π.

关 键 词：Dynamical System Elastic Collisions Reflection Rotation Digits of π 

分 类 号：O35[理学—流体力学]