二次方程化简中坐标轴旋转角的确定问题

从理论上讲,通过坐标轴旋转将二次方程化简为规范形式,从而讨论其曲线的形状,这已是讨论得相当明瞭的课题。但在实际解题中,必须先确定一个合适的旋转角,然后才能进行方程化简。然而,旋转角的确定问题,诸书方法各异,未见有统一详尽的说明。本文针对这一问题做了专门讨论,是一篇数学教育研究论文,可做为中学数学教师和大学《高等数学》课教学的参考。

THE METHODS OF DETERMINING A SPINNING ANGLE OF THE COORDINATE AXES FOR STANDARDIZING A GENERAL QUADRATIC EQUATION

Theoretically speaking, it is a rather-clearly discussed subject to standardize the quadratic equation into the normal forms by spinning the coordinate axis so as to approach the shapes of its curves. But in the practical solution, a proper spinning angle must be first determined before the standar ,dization of the equation is done. However, there are, in all the books, different ways concerning the problem of determining the spinning angle, and there is no united exhaustive explanation of it. This article makes a special discussion of this problem. It is a treatise on mathematics'pedagogy,which may serve as reference for math teachers in the middle school, and for teaching Higher Mathematics at college.