论文部分内容阅读
决赛于5月3日举行,时间三小时半。笔者试拟了这份解答,作为引玉之砖,与广大数学爱好者共同研讨。 第一题 在给定的圆周上随机地选择A、B、C、D、E、F六个点,这些点的选择是独立的,而且相对于弧长而言是等可能的。求ABC、DEF这两个三角形不相交(即没有公共点)的概率。 解:不失一般性,可设圆的直径为1,则周长为π。考虑到对称性,可设A为圆周上定点。设沿逆时
The finals took place on May 3, three and a half hours. The author tried this solution as a brick for introductory jade and discussed it with the majority of math enthusiasts. The first question randomly selects six points A, B, C, D, E, and F on a given circle. The selection of these points is independent, and it is equally possible with respect to the arc length. Find the probability that the two triangles ABC and DEF do not intersect (that is, there is no common point). Solution: Without loss of generality, the diameter of a circle can be set to 1, and the circumference is π. Considering symmetry, we can set A as a fixed point on the circumference. Set along inverse time