问题216——换元,不能改变点的分布的等可能性本问题至截稿时止共收稿15篇.均认为原解法1正确,解法2不妥.来稿认为:解法1的正确性是基于点(a,b)在圆面a2+b2≤1内的分布是均匀的,即点(a,b)落入圆形区域内的任意一处是等可能的;而经过解法2的换元后,点(u,v)落入三角形区域u+v≤1(u≥0,v≥0)内却不是等可能的,要说明这一点颇有难度,它已超出了中学教材的范围, Question 216 - for the yuan, can not change the probability of the distribution of points This question has been received until the time of writing a total of 15. Both that the original solution 1 correct, solution 2 is not correct .Tablet that: the correctness of solution 1 is based on The distribution of point (a, b) in the plane a2 + b2≤1 is uniform, that is, the point (a, b) is likely to fall into any part of the circular region; (U, v) falls into the triangular area u + v ≤ 1 (u ≥ 0, v ≥ 0) but not so possible, to illustrate this quite difficult, it is beyond the scope of secondary school textbooks,