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分数加减法演示

分数加减法演示
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2018-01-25 12:43
函数解析几何几何作图
①本范例通过动态图形演示分数的加法与减法运算过程；②涉及核心数学概念包括分数运算、最小公倍数、几何图形（矩形、圆）的构造与关系；③构造要点：使用Segment, LCM, Sequence, Circle, If, Textfield等命令创建图形元素，通过r, A, c, B, C, D, E, F等对象实现分数的几何表示与运算；④适合初中及以上学生学习分数运算及几何直观，也可用于数学教学演示。

GeoGebra 命令及参数

  1. Segment(E, E + (r, 0)) → r_E
  2. Segment(A, A + (r, 0)) → r_A
  3. Segment(C, C + (r, 0)) → r_C
  4. LCM(d_A, d_C) → LCM_E
  5. Sequence(Rotate[r_E, (360° * k / LCM_E), E], k, 1, LCM_E) → rList_E
  6. Circle(C, r_C) → circle_C
  7. Circle(A, r_A) → circle_A
  8. Sequence(Rotate[A + (r, 0), ((k * 2) * π / d_A), A], k, 0, d_A) → ptList_A
  9. Sequence(Rotate[r_A, (360° * k / d_A), A], k, 1, d_A) → rList_A
  10. Sequence(Sector[circle_A, Element[ptList_A, k], Element[ptList_A, k + 1]], k, 1, n_A) → secList_A
  11. Sequence(Rotate[C + (r, 0), ((k * 2) * π / d_C), C], k, 0, d_C) → ptList_C
  12. Sequence(Sector[circle_C, Element[ptList_C, k], Element[ptList_C, k + 1]], k, 1, n_C) → secList_C
  13. Sequence(Rotate[r_C, (360° * k / d_C), C], k, 1, d_C) → rList_C
  14. Circle(E, r_E) → circle_E
  15. Sequence(Rotate[E + (r, 0), ((k * 2) * π / LCM_E), E], k, 0, LCM_E) → ptList_E
  16. Sequence(Sector[circle_E, Element[ptList_E, k], Element[ptList_E, k + 1]], k, 1, n_E) → secList_E
  17. Circle(F, r_E) → circle_F
  18. Sequence(Rotate[F + (r, 0), ((k * 2) * π / LCM_E), F], k, 0, LCM_E) → ptList_F
  19. If(n_E > LCM_E, n_E - LCM_E, 0) → w
  20. Sequence(Sector[circle_F, Element[ptList_F, k], Element[ptList_F, k + 1]], k, 1, w) → secList_F
  21. Segment(F, F + (r, 0)) → r_F
  22. Sequence(Rotate[r_F, (360° * k / LCM_E), F], k, 1, LCM_E) → rList_F
  23. Textfield(test_d) → InputBox1
  24. Textfield(test_n) → InputBox2
  25. Textfield(max) → InputBox3
  26. If(f_A ≤ f_C, 0, 1) → sw
  27. Sequence(Sector[circle_E, Element[ptList_E, k], Element[ptList_E, k + 1]], k, 1, n_{Esub}) → secList_{Esub}