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对于按照某一法则变化的图形,要求出经过有限次或无限次变化后图形的面积、位置、角变等问题的试题,在各地的中考试题中不断出现.这类题型主要考查学生的思维品质和推理探究能力.解决这类问题的方法,一般是列出表格,从第一次变比开始,依次连续求出几个按法则变化的结果,再探究这些变化结果与变化次数的关系,进而解决问题.现以2012年中考试题为例说明.一、将变化结果用变化次数表示如图1,在标有刻度的直线L上,从点A开始,以AB=1为直径画半圆,记为第1个半圆;以BC=2为直径画半圆,记为第2个半圆;以CD=4为直径画半圆,记为第3个半圆;以DE=8为直径画半圆,记为第4个半圆;……;按此规律,继续画半圆.则第4个半圆的面积
For the graphics that change according to a certain rule, questions that require the area, position and angle change of the graphic after a finite or infinite change are constantly appearing in the middle school entrance examination questions all over the country, which mainly examine students’ thinking Quality and reasoning to explore the ability to solve such problems, the method is generally listed in the table, starting from the first ratio, in turn, to find a few changes in accordance with the law results, and then explore the relationship between these changes and the number of changes, And then solve the problem.Considering the mid-term exam questions in 2012 as an example.First, the results of the change with the number of changes indicated in Figure 1, on the marked line L, starting from the point A, AB = 1 for the diameter drawn semicircle, Marked as the first semicircle; with BC = 2 diameter drawn semicircle, marked as the second semicircle; with CD = 4 diameter drawn semicircle, marked as the first three semicircles; The fourth semicircle; ......; According to this law, continue to draw a semicircle. The fourth semicircle area