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方程平衡模型

方程平衡模型
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2019-06-07 01:40
函数解析几何不等式几何作图滑块动画
①本范例演示通过修改变量值观察方程平衡状态变化的动态模型；②涉及核心数学概念包括方程平衡、变量影响、解析几何；③作图要点：使用Segment、Circle、Intersect、Line、OrthogonalLine、Polygon、Point等GeoGebra命令构建几何图形与交互元素；④适合高中数学教学，用于理解方程解的几何意义及参数变化影响。

GeoGebra 命令及参数

  1. Segment(C, B) → f
  2. Circle(A, 2.5) → c
  3. Intersect(c, f, 1) → D
  4. Intersect(c, f, 2) → E
  5. Segment(D, E) → g
  6. Line(E, eq1) → h
  7. Line(D, eq1) → i
  8. Circle(E, 1) → d
  9. Circle(D, 1) → e
  10. Intersect(e, i, 2) → F
  11. Intersect(d, h, 2) → G
  12. Circle(G, 1.5) → k
  13. Intersect(k, h, 2) → H
  14. Circle(H, 1.5) → p
  15. Intersect(p, h, 2) → I
  16. OrthogonalLine(F, i) → j
  17. OrthogonalLine(G, h) → l
  18. OrthogonalLine(H, h) → m
  19. OrthogonalLine(I, h) → n
  20. Circle(G, 0.5) → q
  21. Circle(H, 0.5) → r
  22. Circle(I, 0.5) → s
  23. Intersect(q, l, 1) → J
  24. Intersect(q, l, 2) → K
  25. Intersect(r, m, 1) → L
  26. Intersect(r, m, 2) → M
  27. Intersect(s, n, 1) → N
  28. Intersect(s, n, 2) → O
  29. OrthogonalLine(K, l) → t
  30. OrthogonalLine(J, l) → b
  31. Circle(J, 1) → c_1
  32. Circle(K, 1) → d_1
  33. Circle(L, 1) → e_1
  34. Circle(M, 1) → f_1
  35. Circle(N, 1) → g_1
  36. Circle(O, 1) → h_1
  37. Intersect(c_1, b, 1) → P
  38. Intersect(d_1, t, 1) → Q
  39. Intersect(e_1, b, 1) → R
  40. Intersect(f_1, t, 1) → S
  41. Intersect(g_1, b, 1) → T
  42. Intersect(h_1, t, 1) → U
  43. Segment(E, G) → i_1
  44. Segment(J, K) → j_1
  45. Segment(K, Q) → k_1
  46. Segment(Q, P) → l_1
  47. Segment(P, J) → m_1
  48. Segment(L, M) → n_1
  49. Segment(R, S) → p_1
  50. Segment(M, S) → q_1
  51. Segment(L, R) → r_1
  52. Segment(N, T) → s_1
  53. Segment(N, O) → t_1
  54. Segment(O, U) → a_1
  55. Segment(U, T) → b_1
  56. Intersect(h, l_1) → V
  57. Intersect(h, p_1) → W
  58. Segment(V, H) → f_2
  59. Segment(W, I) → g_2
  60. Circle(F, a / 5) → c_2
  61. Intersect(c_2, j, 1) → Z
  62. Intersect(c_2, j, 2) → A_1
  63. OrthogonalLine(A_1, j) → h_2
  64. OrthogonalLine(Z, j) → i_2
  65. Circle(A_1, 2.5) → d_2
  66. Circle(Z, 2.5) → e_2
  67. Intersect(e_2, i_2, 1) → B_1
  68. Intersect(d_2, h_2, 1) → C_1
  69. Segment(D, F) → j_2
  70. Segment(Z, A_1) → k_2
  71. Segment(A_1, C_1) → l_2
  72. Segment(C_1, B_1) → m_2
  73. Segment(B_1, Z) → n_2
  74. Polygon(Z, A_1, C_1, B_1) → q1, z_1, p_2, q_2, r_2
  75. Polygon(P, J, K, Q) → q2, p_3, j_3, k_3, q_3
  76. Polygon(L, M, S, R) → q3, l_3, m_3, s_2, r_3
  77. Polygon(N, O, U, T) → q4, n_3, o, u, t_2
  78. Circle(P, 0.3) → c_3
  79. Intersect(c_3, m_1, 1) → D_1
  80. Line(D_1, l_1) → a_2
  81. Circle(D_1, 0.4) → d_3
  82. Intersect(d_3, a_2, 1) → E_1
  83. Circle(R, 0.3) → e_3
  84. Intersect(e_3, r_1, 1) → F_1
  85. Circle(F_1, 0.4) → f_3
  86. Line(F_1, p_1) → b_2
  87. Intersect(f_3, b_2, 2) → G_1
  88. Circle(T, 0.3) → g_3
  89. Intersect(g_3, s_1, 1) → H_1
  90. Circle(H_1, 0.4) → h_3
  91. Line(H_1, b_1) → i_3
  92. Intersect(h_3, i_3, 1) → I_1
  93. Point(n_2) → J_1
  94. Circle(B_1, J_1) → s_3
  95. Line(J_1, m_2) → t_3
  96. Intersect(i, t_3) → K_1
  97. Circle(K_1, 0.1) → c_4
  98. Intersect(c_4, t_3, 2) → L_1