在三角形的三条边上写上三个数a_1~((1)),a_2~((1)),a_3~((1)),然后擦掉这些数,将每边换成刚才另外两边的算术平均值、)即换a_1~((1))为a_1~((2))=a_2~((1))+a_3~((1))/2,换a_3~((1))为a_2~((2))=a_1~((1))+a_3~((1))/2,换a_3~((1))为a_3~((2))=a_~((1))+a_2~((1))/2)据所得各数再作类似计算,如此下去.则1存在(i=1,2,3)且等于a_~((1))+a_2~((1))+a_3~((1))/3。 Write three numbers a_1~((1)), a_2~((1)), a_3~((1)) on the three sides of the triangle. Then erase the numbers and replace each side with the other two sides. Arithmetic mean,) is to change a_1~((1)) is a_1~((2))=a_2~((1))+a_3~((1))/2, and for a_3~((1)) is A_2~((2))=a_1~((1))+a_3((1))/2, change a_3~((1)) to a_3~((2))=a_~((1)) +a_2~((1))/2) According to the obtained numbers, make a similar calculation again, and if so, then 1 exists (i=1, 2, 3) and equal to a_~((1))+a_2~((1 )) +a_3~((1))/3.