RANDOM DISTRIBUTION OF LINES IN A PLANE
RANDOM DISTRIBUTION OF LINES IN A PLANE
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DOI：
10.1103/revmodphys.17.321
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发表时间：
1945-01-01
影响因子：
44.1
通讯作者：
GOUDSMIT, S
中科院分区：
文献类型：
--
作者：
GOUDSMIT, S
事实上，存在错误解释的可能性，因为几个轨道可能意外地似乎来自同一点。玻尔教授曾让我研究几个独立轨道在几乎同一点相交的可能性。幸运的是，在解决这一问题取得任何进展之前，对这一问题的答案的需要已经消失。最近，然而，sameproblem出现在其他连接和在下面我们讨论的第六个步骤迄今为止获得的解决方案。理想化的问题我们考虑一个平面覆盖的直线分布在随机的位置和方向。这些线将平面切割成三角形和多边形。所需要的是碎片面积的概率分布，即碎片的哪一部分具有位于给定界限之间的面积。为了避免无穷大的困难，在一个球面上而不是在一个平面上考虑这个问题似乎是有利的。在这种情况下，球面上的直线被大圆代替。“这些大圆将在随机分布的点上与任意选择的赤道相交，事实上，人们只需要考虑一个半球，因为两个半球是相同的。
ments the possibility existed of erroneous interpretation because several tracks might accidentally seem to originate from the same point. Professor Bohr asked me once to study the chance that several independent tracks intersected at almost the same point. The need for the answer to this problem had fortunately vanished before any progress was made towards its solution. Lately, however, the sameproblem arose in other connections and in the following we discuss the 6rst steps so far obtained towards the solution.THE IDEALIZED PROBLEM We consider a plane covered with straight lines distributed at random in position and direction. These lines cut the plane into triangles and polygons. What is wanted is the probability distribution of the areas of the fragments, namely what fraction of the fragments has an area lying between given limits. In order to avoid difficulties with infinities it seems advantageous to consider the problem on a sphere insteadof in a plane. In that case the straight lines are replaced by great circles on the sphere.'These great circles will intersect an arbitrarily chosen equator at randomly distributed points, in fact one needs to consider only a half sphere as the two halves are identical.