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分数除法演示 by Anthony Dove

分数除法演示 by Anthony Dove
几何画板及绘图内容加载中，请稍等……
2019-04-29 20:55
三角函数解析几何几何作图
①本范例通过动态图形演示了两个真分数的除法过程，直观展示分数除法的几何意义；②涉及核心数学概念包括分数除法运算、相似三角形性质、图形面积计算、周长等；③构造过程中运用了 GeoGebra 命令如 FromBase 创建基础图形，Segment 绘制线段，Circle 绘制圆形，Intersect 计算交点，Point 创建点，Sequence 生成序列，Polygon 绘制多边形，Textfield 添加文本说明，CommonDenominator 计算公分母，Distance 计算距离等；④适合初中及以上数学学习者用于理解分数除法与几何图形的关联，也可用于数学教学演示。

GeoGebra 命令及参数

  1. FromBase(tn_2, 10) → n_2
  2. FromBase(td_1, 10) → d_1
  3. FromBase(td_2, 10) → d_2
  4. Segment(A, A_1) → f1b
  5. Circle(A, 7) → g
  6. Intersect(g, f, 2) → C
  7. Segment(C, A) → h
  8. Point(h) → B
  9. Segment(B, B_1) → f2b
  10. Sequence((x(A) + (i * f2b / d_2), y(A)), i, 1, d_2 - 1) → l2on1b
  11. Sequence((x(A_3) + (i * f2b / d_2), y(A_3)), i, 1, d_2 - 1) → l2on1t
  12. Polygon(A, Element[l2on1b, n_2], Element[l2on1t, n_2], A_3) → Poly3, c_1, c_2, c_3, c_4
  13. Intersect(c_2, c_3) → C_2
  14. Textfield(tn_1) → InputBox1
  15. Textfield(td_1) → InputBox2
  16. Textfield(tn_2) → InputBox3
  17. Textfield(td_2) → InputBox4
  18. Point(j) → E_1
  19. Point(j) → E_2
  20. Segment(E_1, E_2) → e_1
  21. Point(j) → E_3
  22. Point(j) → E_4
  23. Segment(E_3, E_4) → e_2
  24. Point(j) → E_5
  25. Point(j) → E_6
  26. FromBase(tn_1, 10) → n_1
  27. FromBase(tn_3, 10) → n_3
  28. FromBase(td_3, 10) → d_3
  29. FromBase(tm_1, 10) → m_1
  30. Textfield(tm_1) → InputBox5
  31. Textfield(tn_3) → InputBox6
  32. Textfield(td_3) → InputBox7
  33. Segment(A_1, A_2) → f1r
  34. Segment(A_2, A_3) → f1t
  35. Segment(A_3, A) → f1l
  36. Sequence((x(A) + (i * f1b / d_1), y(A)), i, 1, d_1 - 1) → l1b
  37. Sequence((x(A_3) + (i * f1b / d_1), y(A_3)), i, 1, d_1 - 1) → l1t
  38. Sequence(Segment[Element[l1b, i], Element[l1t, i]], i, 1, d_1 - 1) → l1s
  39. Polygon(A, Element[l1b, n_1], Element[l1t, n_1], A_3) → Polyl1, a_1, a_2, a_3, a_4
  40. Segment(B_1, B_2) → f2r
  41. Segment(B_2, B_3) → f2t
  42. Segment(B_3, B) → f2l
  43. Sequence((x(B_3) + (i * f2b / d_2), y(B_3)), i, 1, d_2 - 1) → l2t
  44. Sequence((x(B) + (i * f2b / d_2), y(B)), i, 1, d_2 - 1) → l2b
  45. Sequence(Segment[Element[l2b, i], Element[l2t, i]], i, 1, d_2 - 1) → l2s
  46. Polygon(B, Element[l2b, n_2], Element[l2t, n_2], B_3) → Poly2, b_1, b_2, b_4, b_3
  47. Textfield(tcd) → InputBox8
  48. FromBase(tcd, 10) → cd
  49. CommonDenominator(f_1, f_2) → cd_1
  50. Sequence((x(A) + (i * f1b / cd), y(A)), i, 1, cd - 1) → l1b2
  51. Sequence((x(A_3) + (i * f1b / cd), y(A_3)), i, 1, cd - 1) → l1t2
  52. Sequence(Segment[Element[l1b2, i], Element[l1t2, i]], i, 1, cd - 1) → l1s2
  53. Sequence((x(B) + (i * f1b / cd), y(B)), i, 1, cd - 1) → l2b2
  54. Sequence((x(B_3) + (i * f1b / cd), y(B_3)), i, 1, cd - 1) → l2t2
  55. Sequence(Segment[Element[l2b2, i], Element[l2t2, i]], i, 1, cd - 1) → l2s2
  56. Intersect(c_1, c_2) → C_1
  57. Intersect(b_1, b_2) → C_3
  58. Intersect(b_2, b_4) → C_4
  59. Distance(B, C_3) → distf2
  60. Sequence((x(C_1) + (i * distf2), y(C_1)), i, 0, floor(f_1 / f_2)) → l2divb
  61. Sequence((x(C_2) + (i * distf2), y(C_2)), i, 0, floor(f_1 / f_2)) → l2divt
  62. Sequence(Segment[Element[l2divb, i], Element[l2divt, i]], i, 0, floor(f_1 / f_2)) → l2divs_1
  63. Sequence(Segment[Element[l2divb, i], Element[l2divt, i]], i, 0, f_1 / f_2 + 1) → l2divs
  64. Segment(A_3, A) → Test3
  65. Segment(D, E) → i
  66. Segment(A, Element[l2divb, ceil(f_1 / f_2)]) → Test2_1
  67. LaTeX(Test2_1, true, true) → text8
  68. Segment(A_3, Element[l2divt, ceil(f_1 / f_2)]) → Test1_1