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第二十七届国际中学生数学竞赛的第二题是:“平面上给定△A_1A_2A_2及点P_0,定义As=As_(-3)s≥4,造点列P_0,P_1,P_2,…使得P_(k+1)为绕中心A_(k+1)顺时针旋转120°时,P_k所到达的位置.k=0,1,2….若P_(1986)=P_0,证明△A_1A_2A_3为等边三角形.”此题由我国提供,命题的背景常庚哲老师已写出,本文将利用常老师给出的一些结果,进一步讨论这一类周期点列.
The second question of the 27th International Mathematics Competition for Middle School Students is: “A_1A_2A_2 and P_0 are defined on the plane, As=As_(-3)s≥4 is defined, and P_0, P_1, P_2,... are used to make P_. (k+1) is the position where P_k arrives when rotated 120° clockwise around center A_(k+1).k=0,1,2... If P_(1986)=P_0, prove that △A_1A_2A_3 is equilateral Triangle. "This question is provided by our country. The background of the proposition is written by Chang Gengzhe’s teacher. This article will use some of the results given by Teacher Chang to further discuss this type of periodic sequence.