第27届国际中学生数学竞赛(IMO)试题第2题是中国提供的试题: “平面上给定△A_1 A_2A_3及点P_0,定义A_s=A_(s-3)≥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_1 A_2A_3为等边三角形。” 题中所给的点列有性质P_(1986)=P_0,表明至 The second question of the 27th International Mathematics Competition for Middle School Students (IMO) is the test questions provided by China: “A △ A_1 A_2A_3 and P_0 are defined on the plane, and A_s=A_(s−3)≥4 is defined. P_0, P_1 , P_2, ..., such that P_(k+1) is the position reached by P_k when rotated 120° clockwise around the center A_(k+1). K = 0, 1, 2, ..., if P_ (1986) =P_0, prove that △A_1 A_2A_3 is an equilateral triangle. The list of points given in the question has the property P_(1986)=P_0, indicating that