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分数乘法演示 by Anthony Dove

分数乘法演示 by Anthony Dove
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2019-04-24 01:55
复数几何作图函数图像
①本范例演示了两个真分数相乘的几何意义与计算过程；②涉及核心数学概念包括分数乘法、面积计算、几何表示；③作图要点：使用 GeoGebra 命令如 FromBase, Intersect, Point, Polygon, Segment, Textfield, Sequence, If 构建图形，展示分数乘积的直观理解；④适合初中数学教学，用于帮助学生理解分数乘法的本质。

GeoGebra 命令及参数

  1. FromBase(td_2, 10) → d_2
  2. Intersect(xAxis, yAxis) → A
  3. Point(xAxis) → A_1
  4. Polygon(A, A_1, 4) → poly1, a_1, a_2, a_3, a_4, A_2, A_3
  5. Segment(A_3, A_2) → j_t
  6. Textfield(tn_1) → InputBox1
  7. Textfield(td_1) → InputBox2
  8. Textfield(tn_2) → InputBox3
  9. Textfield(td_2) → InputBox4
  10. Textfield(tn_3) → InputBox5
  11. Textfield(td_3) → InputBox6
  12. Point(j) → E_1
  13. Point(j) → E_2
  14. Segment(E_1, E_2) → e_1
  15. Point(j) → E_3
  16. Point(j) → E_4
  17. Segment(E_3, E_4) → e_2
  18. Point(j) → E_5
  19. Point(j) → E_6
  20. Segment(E_5, E_6) → e_3
  21. FromBase(tn_1, 10) → n_1
  22. FromBase(tn_2, 10) → n_2
  23. FromBase(tn_3, 10) → n_3
  24. FromBase(td_1, 10) → d_1
  25. FromBase(td_3, 10) → d_3
  26. Segment(A, A_3) → j_l
  27. Sequence((x(A), y(A) + (i * j_l / d_1)), i, 0, d_1) → pl
  28. Sequence((x(A_1), y(A_1) + (i * j_l / d_1)), i, 0, d_1) → pr
  29. Sequence(Segment[Element[pl, i], Element[pr, i]], i, 1, d_1 + 1) → list1
  30. Segment(A_2, A_1) → j_r
  31. Sequence((x(A_3) + (i * j_t / d_2), y(A_3)), i, 0, d_2) → pt
  32. Sequence((x(A) + (i * j_t / d_2), y(A)), i, 0, d_2) → pb
  33. Sequence(Segment[Element[pt, i], Element[pb, i]], i, 1, d_2 + 1) → list2
  34. Segment(A, A_1) → j_b
  35. Intersect(Element[list2, n_2 + 1], j_b) → P_1
  36. Intersect(Element[list2, n_2 + 1], Element[list1, n_1 + 1]) → P_2
  37. Polygon(A, Element[pl, n_1 + 1], P_2, P_1) → Poly_{Sol}, P_{Sola}, P_{Solb}, P_{Solc}, P_{Sold}
  38. Sequence((x(P_1), y(P_1) + (i * j_r / d_1)), i, 0, d_1) → list3
  39. Sequence(Segment[Element[pl, i], Element[list3, i]], i, 1, d_1 + 1) → list_{sol}
  40. Polygon(A, Element[pl, n_1 + 1], Element[pr, n_1 + 1], A_1) → Poly_{First}, P_{1d}, P_{1a}, P_{1b}, P_{1c}
  41. Polygon(A, A_3, Element[pt, n_2 + 1], P_1) → Poly_{Sec}, P_{2a}, P_{2b}, P_{2c}, P_{2d}
  42. FromBase(td_4, 10) → d_4
  43. Textfield(tn_4) → InputBox3_1
  44. Textfield(td_4) → InputBox4_1
  45. FromBase(tn_4, 10) → n_4
  46. FromBase(td_5, 10) → d_5
  47. Textfield(tn_5) → InputBox1_1
  48. Textfield(td_6) → InputBox2_1
  49. Textfield(tn_6) → InputBox3_2
  50. Textfield(td_5) → InputBox4_2
  51. FromBase(tn_5, 10) → n_5
  52. FromBase(tn_6, 10) → n_6
  53. FromBase(td_6, 10) → d_6
  54. If(c ≟ 1 ∧ d ≟ 1, d ≟ 0, d ≟ 1) → e