在曲线的极坐标方程这一节教学内容结束后,几个学生用几何画板作出极坐标系中的几个方程图像(如图1),并兴奋地告诉了笔者他们的发现:对于极坐标方程ρ=sin(κθ)(κ∈N~*),当变量θ的系数为奇数时,花瓣的叶数正好等于系数,当变量θ的系数为偶数时,花瓣的叶数是系数的2倍.为什么会这样呢?笔者借助几何画板进行一番探究与思考,发现了一些有趣的结论,现整理出来,与读者朋友们分享. After the course of the curvilinear polar equation equation ends, several students use geometry panels to make several equations in the polar coordinate system (Figure 1) and excitedly tell the author what they found: For the polar equation ρ = sin (κθ) (κ∈N ~ *). When the coefficient of variable θ is odd, the leaf number of the petal equals the coefficient. When the coefficient of the variable θ is even, the leaf number of the petal is twice as large as the coefficient. Why does this happen? I draw on geometric Sketchpad for some exploration and reflection, found some interesting conclusions, is now sorted out, and readers to share.