基于圆柱体骰子三面概率落地均匀性探究

Landing uniformity Exploration of the probability of three sides of cylinder

传统硬币正反面落地概率分别趋近于1/2,而侧面落地概率几乎为0.本文为了探究新型圆柱形骰子三面落地概率均匀的影响因素,从力学角度对圆柱形骰子发生弹性碰撞和非弹性碰撞的运动过程进行了理论分析,将影响落地概率均匀性的因素分为圆柱形骰子自身的物理和几何特征以及外部影响因素,通过建立各类圆柱形骰子模型,采用控制变量法进行实验,并应用软件进行仿真模拟,所得实验结论和仿真结论与理论分析吻合.研究表明骰子厚度直径比、接触面材质硬度、抛掷高度及圆柱体重心线与竖直方向向量夹角是影响落地概率均匀性的主要因素.

The probability of landing on the front and back of traditional coin approaches 1/2 respectively,while the probability of landing on the side is almost zero.In order to explore the factors affecting the probability of landing evenly on three sides of a new type of cylindrical dice,kinematic process of elastic collision and inelastic collision of cylindrical dice are theoretically analyzed from the perspective of mechanics,and the factors affecting the probability of landing evenly are divided into physical and geometric characteristics of cylindrical dice and external influencing factors.By establishing various types of cylindrical dice models,the control variable method is used to carry out the experiment and the software is used to carry out the simulation.The experimental and simulation results are agreement with the theoretical analysis.The results show that the thickness to diameter ratio,the hardness of contact surface material,the throwing height and the angle between the center of gravity of the cylinder and the vertical direction vector are the main factors affecting the uniformity of landing probability.