几何作图题的代数分析法,即设图已作出,利用图形的性质(包括辅助图形),用代数的方法,求出未知线段与已知线段的关系式,然后,再根据关系式作出所求。这对于培养学生的独立思维能力,提高学习的趣味,无疑起着积极的作用。数学家高斯正是由于作出了正十七边形,才坚定地献身于数学研究。当然,盲目地设想一些已证实不可能的问题,势必会碰壁的。如,不能用尺规,把立方体的体积扩大一倍,把任意角三等分,作等于已知圆的面积的正方形,正七边形,正九边形和一些无几何意义的代数式 Algebraic analysis of the geometry of the problem, that is, plans have been made, the use of the nature of the graphics (including auxiliary graphics), using algebraic method to find the relationship between unknown line segments and known lines, and then, according to the relationship begging. This is undoubtedly playing a positive role in cultivating students' independent thinking skills and improving their learning interest. It is precisely because mathematician Gauss made a positive seventeen polygons that he was firmly committed to mathematical studies. Of course, blindly envisaging problems that have proven impossible will inevitably run into trouble. For example, you can not use the ruler to double the volume of a cube, divide an arbitrary angle into three equal parts, squares equal to the area of ​​a known circle, regular heptagon, regular nine, and some geometric expressions