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Equation Balance Model

Equation Balance Model
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2019-06-07 01:40
FunctionCoordinate GeometryInequalityGeometric ConstructionSlider Animation
This example demonstrates a dynamic model where students modify variable values to observe changes in equation balance. Core math concepts include equation equilibrium, variable impact, and analytical geometry. Constructed using commands like Segment, Circle, Intersect, Line, OrthogonalLine, Polygon, Point in GeoGebra, suitable for high school mathematics teaching to understand the geometric meaning of equation solutions and the effects of parameter changes.

GeoGebra Commands & Parameters

  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