“变中不变”是许多数学知识本质的重要体现.例如直线和圆的位置关系千变万化,却往往能动中蕴静,于不确定的动态中隐含恒定不变的量,充满了哲学意味.如果用动画演示这种变化过程,就能够明显地发现其中的静态特征.可如果仅依靠思维从纷乱的动态和繁杂的运算中找出隐匿的定值,往往使学生望而生畏,思而不前.然而,如果从方程的角度理解这个问题,把握住动中藏静体现在方程上的实质,便能 “Invariable” is an important manifestation of the nature of many mathematical knowledge. For example, the positional relationship between lines and circles is ever-changing, but it is often able to move in the implicit, implying a constant amount in the uncertainty of the dynamic, full of philosophy It means that if you use animation to demonstrate this process of change, you can clearly find the static features. If you only rely on thinking to find hidden values ​​from chaotic dynamics and complicated calculations, students will often be daunted, not thinking. Ex. However, if we understand this problem from the perspective of equations, we can grasp the essence of the equation in motion, and we can