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圆与数列的变换演示

圆与数列的变换演示
几何画板及绘图内容加载中，请稍等……
2017-03-12 13:02
圆数列解析几何函数图像
①本范例通过动态演示圆与数列的变换关系，直观展示几何图形的平移与参数变化；②涉及核心数学概念包括指数函数、抛物线、平移变换、面积计算、坐标系及直方图；③作图要点运用了Circle（圆）、Sequence（数列）等GeoGebra命令，通过滑块控制参数变化，实现动态效果；④适合高中数学教学，用于理解函数图像变换、参数方程及解析几何应用。

GeoGebra 命令及参数

  1. Circle((0, 0), 1) → r1
  2. Sequence(Rotate[Dilate[r1, f(a1), (1, 0)], (k * a1), (0, 0)], k, 0, n1 - 1) → r2
  3. Sequence(Rotate[Dilate[r2, f(a2), (1, 0)], (k * a2), (0, 0)], k, 0, n2 - 1) → r3
  4. Sequence(Rotate[Dilate[r3, f(a3), (1, 0)], (k * a3), (0, 0)], k, 0, n3 - 1) → r4
  5. Sequence(Rotate[Dilate[r4, f(a4), (1, 0)], (k * a4), (0, 0)], k, 0, n4 - 1) → r5
  6. Sequence(Rotate[Dilate[r5, f(a5), (1, 0)], (k * a5), (0, 0)], k, 0, n5 - 1) → r6
  7. Sequence(Rotate[Dilate[r1, f(a5), (1, 0)], (k * a5), (0, 0)], k, 0, n5 - 1) → C1
  8. Sequence(Rotate[Dilate[r1, f(a4), (1, 0)], (k * a4), (0, 0)], k, 0, n4 - 1) → C2
  9. Sequence(Rotate[Dilate[C2, f(a5), (1, 0)], (k * a5), (0, 0)], k, 0, n5 - 1) → C3
  10. Sequence(Rotate[Dilate[r1, f(a3), (1, 0)], (k * a3), (0, 0)], k, 0, n3 - 1) → C4
  11. Sequence(Rotate[Dilate[C4, f(a4), (1, 0)], (k * a4), (0, 0)], k, 0, n4 - 1) → C5
  12. Sequence(Rotate[Dilate[C5, f(a5), (1, 0)], (k * a5), (0, 0)], k, 0, n5 - 1) → C6
  13. Sequence(Rotate[Dilate[r1, f(a2), (1, 0)], (k * a2), (0, 0)], k, 0, n2 - 1) → C7
  14. Sequence(Rotate[Dilate[C7, f(a3), (1, 0)], (k * a3), (0, 0)], k, 0, n3 - 1) → C8
  15. Sequence(Rotate[Dilate[C8, f(a4), (1, 0)], (k * a4), (0, 0)], k, 0, n4 - 1) → C9
  16. Sequence(Rotate[Dilate[C9, f(a5), (1, 0)], (k * a5), (0, 0)], k, 0, n5 - 1) → C10