蒙特卡罗方法实验设计

介绍蒙特卡罗方法计算维维安尼体的实验设计过程，应用计算机随机模拟方法计算确定的空间立体体积，给出实现该方法的计算程序代码。将实验数据结果列表，分析数据变化规律。验证了误差实验数据服从正态分布的规律性。为了揭示蒙特卡罗方法对多维问题计算的有效性，文中例举了三维或四维问题作为实验设计题目，其中包括牟合方盖问题、飞碟体积问题以及n维球体问题。最后介绍了一类数学软件Matlab和实验报告写作规范。

Experimental Design of Monte Carlo Method

This paper introduces the progress of experimental design of solving the Viviani body problem by Monte Carlo method. The volume of a certain three-dimension is calculated by computer random simulation, hence to present the program code. Then, we list the data of the experiment result, and analyze the data. The regularity of experimental error data complying with the normal distribution is identified. In order to show that Monte Carlo method is efficient to the solution of multi-dimensional problems, three-dimensional or four-dimensional problems will be given as the experimental design questions, including the Steinmetz Solid problem, the UFO volume problem, and n-dimensional ball problem. In the end, we will introduce the Matlab, a kind of Math software, and the specification of the experimental reports.