关于圆上随机弦奇论问题的解析  

Random string singularity theory on circles

作　　者：郑长波[1] 孟宪涛[2] 

机构地区：[1]大连海洋大学,辽宁大连116300 [2]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2012年第2期164-167,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省教育厅科学研究资助项目(20060842)

摘　　要：介绍了圆上随机弦的贝特朗奇论问题,由于弦的做法具有任意性,构造出5种不同的随机弦,按照每一种随机弦的构造方法分别求解其奇论问题,得到了7种解法。然后进行奇论解析,分析其一个问题有无穷答案的原因之一是随机弦构造方法的不同并对其进行具体阐述,其二是计算概率P所确定随机试验有差异。通过分析,出现同一个问题多种答案的直接原因是各个解法在计算概率时所依据的随机试验是相异的,根本原因则是人们对构造随机弦任意性理解的不同,共同点是随机点在基本事件空间内都是均匀分布。得到对随机弦的"任意"性不同理解的7种解法的相应结果是正确的,奇论问题并不"奇",在三维球体中仍有相应的Bertrand奇论存在。This article describes the Beit Lucky strange problems on circle of random strings. According to the arbitrary of practice, five constructors of random string have been obtained, and on the basis of constructor of each random string, the strange problem is solved, and seven solutions have been got. Basing on the construction methods of different random strings, this paper concludes that strange problems have an infinite number of results. One of the reasons that a problem with an infinite number of answers is the different construction methods of random strings, and the second is to calculate the probability P of the randomized trials to determine the differences. By analyzing each solution in the calculation of probability, the paper finds the direct cause of a problem with a variety of answers is that the use of randomized trials during the calculation of probability are dissimilar, and the fundamental reason is the different understanding structure of the arbitrary in constructing random string for different people, and the conclusion seven solutions of different random strings with different understanding are absolutely correct, and actually, strange problem is not strange; there be three dimension spheres with corresponding in Bertrand.

关 键 词：随机弦 随机试验 几何概率 奇论 

分 类 号：O312[理学—一般力学与力学基础]