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《中小学数学》(初中版)2012年第5期《用数轴上的点表示形如a~(1/2)的数》一文,介绍了利用勾股定理,借助于在数轴上画出直角三角形,进而再作出表示a~(1/2)的点.文中的作法有独到之处,既简单直观,又容易操作,但该文的作法也有不足之处,即被开方数a只能局限于正整数的情形.其实在数轴上作出表示a~(1/2)的点还有不同的方法,且被开方数可不局限于正整数,现把作法介绍如下.我们先来看如下问题:如图1,在直角坐标系中,设OB=a,OC=1,P为BC的中点,在横轴上取一点A使AP=CP,那么AP=CP=(a+1)/2,
“Elementary and middle school mathematics” (junior high school edition) 2012 fifth issue “with the number of points on the axis representation of a ~ (1/2) number of” article, introduced the use of Pythagorean theorem, by drawing a right angle Triangles, and then make a point that represents a ~ (1/2) .This paper has its own unique method of practice, which is simple and intuitive, and easy to operate. However, Is limited to the case of a positive integer. In fact, the number of axes to make that a ~ (1/2) points and there are different ways, and the square is not limited to a positive integer, the practice is introduced below. Problem: As shown in Fig. 1, in the Cartesian coordinate system, let OB = a, OC = 1, P be the midpoint of BC, take a point A on the horizontal axis to make AP = CP, then AP = CP = /2,