反演变换在尺规作图中的应用

The application of inversion in construction with ruler and compasses

给出了一种作已知三圆之切圆的尺规作图方法.该方法基于初等平面几何的反演变换,通过反演变换,较难解决的用直尺和圆规作圆锥曲线的问题被转换为用直尺和圆规作直线的问题.在此种解题方法的基础上,结合其他事例,进一步阐释了采用变换方法解决数学问题的思想.

The article presents a method to get the tangent circle of certain three given circles with ruler and compasses, and the method is based on inversion of primary planimetry. Inversion makes the difficult problem about conic construction with ruler and compasses can be changed into problem of linear construction. Analyzing the procedure of solution, we reemphasize idea of inversion which acts as important role in many field of problem solving