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两种溶液混合的百分比问题动态演示

两种溶液混合的百分比问题动态演示
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2015-08-11 15:43
多边形函数数列滑块动画函数图像
所属专题 Chemistry2
该范例通过GeoGebra动态几何环境，直观演示了两种不同浓度溶液混合后百分比变化的数学建模过程。核心数学概念涉及比例、百分比、线性关系以及函数图像，通过滑块和动态文本实时更新混合后的浓度值。作图要点包括使用OrthogonalLine、Line、Intersect等命令构造坐标轴和辅助线，利用Sequence、KeepIf、Element、IndexOf等命令处理数据列表，并通过Textfield、Segment、Midpoint、VerticalText等对象创建交互界面，最终用Polygon和Ray绘制图形区域。适合初中高年级至高中学生理解溶液混合问题，也可用于数学建模或化学跨学科教学，帮助学生将抽象的比例关系可视化。

GeoGebra 命令及参数

  1. OrthogonalLine(G_2, l) → q
  2. Line(A_2, C_2) → p
  3. Intersect(q, p) → B_2
  4. Sequence((100 * n), n, 0, 200) → list1
  5. Line(A_3, B_3) → f
  6. Intersect(c, f) → C_3
  7. KeepIf(0 < x ≤ 100, list21) → list31
  8. Element(list31, 1) → elem1
  9. IndexOf(elem1, list21) → index1
  10. Element(list1, index1) → scale
  11. Line(A_1, C_1) → b
  12. Intersect(a, b) → B_1
  13. Line(B_4, C_4) → i
  14. Intersect(l, i) → A_4
  15. Textfield(m_{11}) → inputBoxm11
  16. Textfield(m_{21}) → inputBoxm21
  17. Textfield(w_{21}) → inputBoxw21
  18. Textfield(w_{11}) → inputBoxw11
  19. Textfield(m_{32}) → inputBoxm32
  20. Segment(E_1, C_1) → b_1
  21. Segment(C_1, F_1) → c_1
  22. Segment(D_1, B_1) → a_1
  23. Segment(B_1, G_1) → d_1
  24. Segment(G_2, B_2) → d_2
  25. Segment(B_2, D_2) → a_2
  26. Segment(C_2, E_2) → b_2
  27. Segment(C_2, F_2) → c_2
  28. Segment(G_3, B_3) → d_3
  29. Segment(D_3, B_3) → a_3
  30. Segment(G_4, B_4) → d_4
  31. Segment(B_4, D_4) → a_4
  32. Segment(F_4, C_4) → c_4
  33. Segment(C_4, E_4) → b_4
  34. Segment(A_4, C_4) → g_4
  35. Midpoint(D_2, E_2) → S_2
  36. Midpoint(D_4, E_4) → S_4
  37. Textfield(w_{12}) → inputBoxw12
  38. Textfield(w_{22}) → inputBoxw22
  39. Textfield(w_{13}) → inputBoxw13
  40. Textfield(w_{23}) → inputBoxw23
  41. Textfield(w_{33}) → inputBoxw33
  42. Textfield(m_{13}) → inputBoxm13
  43. Textfield(w_{32}) → inputBoxw32
  44. Textfield(w_{14}) → inputBoxw14
  45. Textfield(w_{34}) → inputBoxw34
  46. Textfield(m_{14}) → inputBoxm14
  47. Textfield(m_{34}) → inputBoxm34
  48. Midpoint(D_1, E_1) → S_1
  49. VerticalText(Oy) → Oyv
  50. VerticalText(text2) → text3
  51. Min(w_{13}, w_{23}) → min3
  52. Max(w_{13}, w_{23}) → max3
  53. Polygon(H_1, H_2, J_2, J_1) → poly1z1, a_5, b_5, c_5, d_5
  54. Polygon(H_1, H_2, I_2, I_1) → poly1b1, d, e, j, k
  55. Midpoint(D_3, E_3) → S_3
  56. Ray(F_3, C_3) → h
  57. Polygon(H_3, H_4, J_4, J_3) → poly1z2, n_1, o_1, t_5, r_5
  58. Polygon(H_3, H_4, I_4, I_3) → poly1b2, n_2, o_2, p_5, q_5
  59. Polygon(H_8, H_9, I_9, I_8) → poly1b3, u_5, v_1, w_5, x_1
  60. Polygon(H_8, H_9, J_9, J_8) → poly1z3, u_6, v_2, z_1, y_1
  61. Segment(F_3, C_3) → c_3
  62. Segment(C_3, E_3) → b_3
  63. OrthogonalLine(F_2, l) → g
  64. Polygon(H_5, H_7, I_7, I_5) → poly1, h_5, h_7, i_7, i_5
  65. Polygon(H_5, H_6, J_6, J_5) → poly2, h_1, h_6, j_6, j_5
  66. Polygon(H_6, H_7, J_7, J_{61}) → poly3, m, n, t_6, e_1
  67. Segment(H_6, I_6) → i_1
  68. Segment(A_3, C_3) → j_1
  69. Segment(A_1, C_1) → l_1
  70. Segment(A_2, C_2) → e_2