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Equation Balance Demonstration

Equation Balance Demonstration
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2015-04-29 01:07
VectorFunctionCoordinate GeometryGeometric ConstructionGraphing
This example dynamically demonstrates the principle of equation balance, visually presenting the symmetric relationship between both sides of an equation; core math concepts include linear functions, polynomial functions, binomial distribution, and 3D vectors; construction highlights from the summary utilize commands/objects like Segment, Point, CountIf, Circle, OrthogonalLine, Polygon, Sum in GeoGebra; suitable for high school and above learners to understand equation balance and function graph transformations.

GeoGebra Commands & Parameters

  1. Segment(V_2, W_2) → j_2
  2. Point(j_2) → D_3
  3. Point(j_2) → C_3
  4. Point(j_2) → Z_2
  5. CountIf(x > 0, B27:B29) → B31
  6. Segment(E, F) → c
  7. Point(c) → T
  8. Point(c) → S
  9. Point(c) → R
  10. Point(c) → Q
  11. Segment(C, D) → b
  12. Point(b) → P
  13. Point(b) → N
  14. Point(b) → M
  15. Point(b) → L
  16. CountIf(x < 0, B17:B20) → B24
  17. Segment(A, B) → a
  18. Point(a) → K
  19. Point(a) → J
  20. Point(a) → I
  21. Point(a) → O
  22. CountIf(x > 0, B1:B8) → B14
  23. Segment(Q_3, R_3) → k_2
  24. Point(k_2) → T_3
  25. Point(k_2) → S_3
  26. CountIf(x > 0, A28:A29) → A32
  27. Segment(A_1, B_1) → i
  28. Point(i) → E_1
  29. CountIf(x > 0, A13:A13) → A14
  30. Point(i) → D_1
  31. Point(i) → C_1
  32. CountIf(x > 0, A7:A8) → A10
  33. Segment(G, H) → d
  34. Point(d) → Z
  35. Point(d) → W
  36. Point(d) → V
  37. Point(d) → U
  38. CountIf(x > 0, A19:A22) → A25
  39. Segment(A_2, B_2) → a_1
  40. Circle(Q, 0.5) → e
  41. Circle(R, 0.5) → f
  42. Circle(S, 0.5) → g
  43. Circle(T, 0.5) → h
  44. Circle(I, 0.5) → k
  45. Circle(J, 0.5) → p
  46. Circle(K, 0.5) → q
  47. Circle(O, 0.5) → r
  48. Circle(U, 0.5) → s
  49. Circle(V, 0.5) → t
  50. Circle(W, 0.5) → c_1
  51. Circle(Z, 0.5) → d_1
  52. Segment(F_1, G_1) → j
  53. OrthogonalLine(C_1, i) → l
  54. OrthogonalLine(D_1, i) → m
  55. OrthogonalLine(E_1, i) → n
  56. Point(Circle[C_1, 2.000099997500125]) → H_1
  57. Polygon(C_1, H_1, I_1, J_1) → poly1, c_2, h_1, i_1, j_1
  58. Point(Circle[D_1, 2]) → K_1
  59. Polygon(D_1, K_1, L_1, M_1) → poly2, d_2, k_1, l_1, m_1
  60. Point(a_1) → J_2
  61. Point(a_1) → K_2
  62. Point(a_1) → O_1
  63. Segment(A_3, B_3) → a_2
  64. Point(a_2) → I_3
  65. Point(a_2) → K_3
  66. Point(a_2) → O_2
  67. Segment(A_4, B_4) → a_3
  68. Point(a_3) → I_4
  69. Point(a_3) → J_4
  70. Point(a_3) → O_3
  71. Point(Circle[L, 0.8280096617793782]) → N_1
  72. Polygon(L, N_1, P_1) → poly3, p_1, l_2, n_1
  73. Point(Circle[M, 0.7161005515987262]) → Q_1
  74. Polygon(M, Q_1, R_1) → poly4, r_1, m_2, q_1
  75. Point(Circle[N, 0.6997142273814358]) → S_1
  76. Polygon(N, S_1, T_1) → poly5, t_1, n_2, s_1
  77. Point(Circle[P, 0.7211102550927978]) → U_1
  78. Polygon(P, U_1, V_1) → poly6, v_1, p_2, u_1
  79. Point(xAxis) → W_1
  80. Point(xAxis) → D_2
  81. Polygon(W_1, Z_1, C_2, D_2) → poly7, w_1, z_1, c_3, d_3
  82. Point(Circle[E_1, 2.0502987587178603]) → E_2
  83. Polygon(E_1, E_2, F_2, G_2) → poly8, e_1, e_2, f_2, g_2
  84. Point(yAxis) → H_2
  85. Point(d_3) → I_2
  86. Point(yAxis) → L_2
  87. Point(d_3) → M_2
  88. Segment(L_2, M_2) → b_1
  89. Point(d_3) → N_2
  90. Segment(L_2, N_2) → f_1
  91. Segment(M_2, N_2) → g_1
  92. Polygon(L_2, M_2, N_2) → poly9, n_3, l_3, m_3
  93. Segment(P_2, Q_2) → b_2
  94. Segment(R_2, S_2) → h_2
  95. Sum(C3:C6) → C8
  96. CountIf(x > 0, C12:C12) → C13
  97. CountIf(x > 0, D12:D12) → D13
  98. Segment(T_2, U_2) → i_2
  99. Point(Circle[Z_2, 1.8080613758656188]) → E_3
  100. Polygon(Z_2, E_3, F_3, G_3) → poly10, z_2, e_3, f_3, g_3
  101. Point(Circle[C_3, 1.697060394712511]) → H_3
  102. Polygon(C_3, H_3, J_3, L_3) → poly11, c_4, h_3, j_3, l_4
  103. Point(Circle[D_3, 1.765030632264185]) → M_3
  104. Polygon(D_3, M_3, N_3, P_3) → poly12, d_4, m_4, n_4, p_3
  105. Point(Circle[S_3, 0.7572989883260863]) → U_3
  106. Polygon(S_3, U_3, V_3) → poly13, v_3, s_3, u_3
  107. Point(Circle[T_3, 0.7697908875840829]) → W_3
  108. Polygon(T_3, W_3, Z_3) → poly14, z_3, t_3, w_3
  109. Point(f_1) → C_4
  110. Point(d_3) → D_4
  111. Polygon(C_4, D_4, 3) → poly15, q_2, r_2, s_2, E_4