基于MATLAB的Galton板实验仿真设计及实现  

Design and Development of Galton Board Trial Based on MATLAB

作　　者：李林[1] 张树义[1] 

机构地区：[1]北京大学数学科学学院数学与应用数学实验室,北京100871

出　　处：《计算机仿真》2006年第3期243-246,共4页Computer Simulation

基　　金：北京大学数学与应用数学教育部开放实验室基金资助(2004-01)

摘　　要：Galton板作为一种简单可行的教具,在高中、大学的有关教材中都有所介绍。它在热物理学与概率论的教学中发挥着积极有效的演示作用。但是现有的关于Galton板的定量分析较为贫乏和粗略。该文首先介绍了Galton板的结构、实验现象和物理背景,然后建立了细致的概率模型,从本质上对实验现象进行了分析,从而给出理论上的合理解释。该文通过使用MATLAB中的若干工具包,开发了用户图形界面等仿真程序,针对不同的概率情形模拟了Galton板的实验结果,从而验证了相应的理论结果,也表明了MATLAB在实验仿真中的强大用途。As a simple and convenient teaching aid, Galton board is widely introduced in textbooks of high schools and universities. It appears in the teaching of thermodynamics and probability theory as an effective demonstration. However, the present quantitative analysis is inconsistently lacking. This paper first introduces the structure, experimental phenomena and physical background of Galton board, establishes elaborately a probabilistic model to analyze the phenomena essentially, and provides reasonable theoretical explanations. Emulational software based on GUI is developed using several toolboxes in MATLAB. Experimental results are simulated for different probability settings and accordingly prove the theoretical results. It also shows that MATLAB is useful in the field of simulation.

关 键 词：伽尔顿板 最概然分布 二项分布 中心极限定理 

分 类 号：TP319.9[自动化与计算机技术—计算机软件与理论]