1.引言近几年来,各地中考和比赛[1,2]中出现了关于下面n阶奇异矩形的试题,旨在考查学生的归纳推理能力.一张矩形纸片,剪下一个正方形,剩下一个矩形,称为第一次操作;在剩下的矩形纸片中再剪下一个正方形,剩下一个矩形,称为第二次操作;…;若在第n次操作后,剩下的矩形为正方形,则称原矩形为n阶奇异矩形.如图1,矩形ABCD中,若AB=2,BC=6,则称矩形ABCD为2阶奇异矩形. 1. INTRODUCTION In recent years, questions about the following n-th singularity rectangle appeared in the entrance exams and competitions [1, 2] to examine students’ abilities of inductive reasoning. A rectangular piece of paper cut out a square and left A rectangle, called the first operation; in the remaining rectangular paper and then cut a square, leaving a rectangle, called the second operation; ...; If after the n-th operation, the remaining rectangle For the square, then said the original rectangular n-order singular rectangle.As shown in Figure 1, the rectangle ABCD, if AB = 2, BC = 6, then said rectangular ABCD for the second-order singular rectangle.