MathPlotAI Logo MathPlotAI

Building Models with Cubes

Building Models with Cubes
Loading the math board and drawing, please wait…
2020-04-10 01:57
MatrixTransformationGeometric Construction
This example demonstrates how to construct various models using cubes. It involves core mathematical concepts such as random variables, matrices, and similarity transformations. Using GeoGebra commands like AttachCopyToView, Polygon, Intersect, Segment, and Point, complex geometric shapes can be constructed. Suitable for middle school students and teachers.

GeoGebra Commands & Parameters

  1. AttachCopyToView(PolyLine[(4.64,0.74), (4.64,0.84), (4.64,0.92), (4.64,1.02), (4.64,1.14), (4.64,1.3), (4.64,1.38), (4.64,1.46), (4.66,1.54), (4.66,1.62), (4.68,1.68), (4.74,1.72), (4.82,1.66), (4.82,1.5), (4.82,1.4), (4.82,1.28), (4.82,1.2), (4.84,1.1), (4.86,1.04), (4.86,0.94), (4.86,0.84), (4.86,0.74), (4.86,0.64), (4.92,0.74), (4.92,0.82), (4.92,0.9), (4.92,1), (4.92,1.14), (4.92,1.22), (4.92,1.32), (4.92,1.4), (4.92,1.5), (4.94,1.56), (5,1.52), (5.02,1.44), (5.06,1.34), (5.08,1.26), (5.08,1.18), (5.1,1.12), (5.1,1.04), (5.1,0.94), (5.12,0.86), (5.14,0.76), (5.14,0.68), (5.16,0.62), (5.18,0.68), (5.18,0.76), (5.18,0.84), (5.18,0.94), (5.2,1.04), (5.22,1.12), (5.24,1.18), (5.26,1.26), (5.26,1.34), (5.26,1.44), (5.26,1.52), (5.26,1.6), (5.3,1.54), (5.32,1.48), (5.36,1.38), (5.38,1.3), (5.4,1.22), (5.42,1.16), (5.44,1.1), (5.46,1.04), (5.48,0.96), (5.5,0.9), (5.52,0.84), (5.52,0.74), (5.54,0.86), (5.54,0.98), (5.54,1.12), (5.54,1.2), (5.52,1.3), (5.52,1.38), (5.52,1.48), (5.52,1.4), (5.6,1.32), (5.64,1.26), (5.7,1.18), (5.72,1.1), (5.74,1.02), (5.76,0.96), (5.78,0.9), (5.8,0.82), (5.8,0.74), (NaN,NaN), true], 1, (-4.300000000000001, -2.6600000000000015), (6.5000000000000036, 6.3), (0, 448), (540, 0)) → stroke1
  2. Polygon(A, B, 4) → poly1, f, g, h, k, C, D
  3. Polygon(B, E, 4) → poly2, p, q, r, s, J, K
  4. Polygon(E, L, 4) → poly3, t, a, b, c, M, N
  5. Polygon(D, C, 4) → poly4, d, e, i_1, j_1, O, P
  6. Polygon(C, J, 4) → poly5, k_1, l_1, m_1, n_1, Q, R
  7. Polygon(J, M, 4) → poly6, p_1, q_1, r_1, s_1, S, T
  8. Polygon(P, O, 4) → poly7, t_1, a_1, b_1, c_1, U, V
  9. Polygon(O, Q, 4) → poly8, d_1, e_1, f_2, g_2, W, Z
  10. Polygon(Q, S, 4) → poly9, h_2, i_2, j_2, k_2, A_1, B_1
  11. Intersect(f, k) → C_1
  12. Segment(C_1, D_1) → l_2
  13. Intersect(i_2, j_2) → E_1
  14. Segment(D_1, E_1) → m_2
  15. Intersect(b_1, c_1) → F_1
  16. Segment(E_1, F_1) → n_2
  17. Segment(F_1, C_1) → p_2
  18. Intersect(f, g) → G_1
  19. Intersect(a_1, b_1) → H_1
  20. Segment(G_1, H_1) → q_2
  21. Intersect(e_1, f_2) → I_1
  22. Intersect(p, q) → J_1
  23. Segment(I_1, J_1) → r_2
  24. Intersect(h, k) → K_1
  25. Intersect(a, b) → L_1
  26. Segment(K_1, L_1) → s_2
  27. Intersect(i_1, j_1) → M_1
  28. Intersect(q_1, r_1) → N_1
  29. Segment(M_1, N_1) → t_2
  30. Polygon(O_1, P_1, 4) → poly10, a_2, b_2, c_2, d_2, Q_1, R_1
  31. Polygon(P_1, S_1, 4) → poly11, e_2, f_3, g_3, h_3, T_1, U_1
  32. Polygon(S_1, V_1, 4) → poly12, i_3, j_3, k_3, l_3, W_1, Z_1
  33. Polygon(R_1, Q_1, 4) → poly13, m_3, n_3, p_3, q_3, A_2, B_2
  34. Polygon(Q_1, T_1, 4) → poly14, r_3, s_3, t_3, a_3, C_2, D_2
  35. Polygon(T_1, W_1, 4) → poly15, b_3, c_3, d_3, e_3, E_2, F_2
  36. Polygon(B_2, A_2, 4) → poly16, f_4, g_4, h_4, i_4, G_2, H_2
  37. Polygon(A_2, C_2, 4) → poly17, j_4, k_4, l_4, m_4, I_2, J_2
  38. Polygon(C_2, E_2, 4) → poly18, n_4, p_4, q_4, r_4, K_2, L_2
  39. Intersect(h_4, i_4) → M_2
  40. Intersect(p_4, q_4) → N_2
  41. Segment(M_2, N_2) → s_4
  42. Segment(N_2, O_2) → t_4
  43. Intersect(a_2, d_2) → P_2
  44. Segment(O_2, P_2) → a_4
  45. Segment(P_2, M_2) → b_4
  46. Intersect(g_4, h_4) → Q_2
  47. Segment(Q_2, R_2) → c_4
  48. Intersect(e_2, f_3) → S_2
  49. Intersect(k_4, l_4) → T_2
  50. Segment(S_2, T_2) → d_4
  51. Intersect(c_2, d_2) → U_2
  52. Intersect(j_3, k_3) → V_2
  53. Segment(U_2, V_2) → e_4
  54. Intersect(c_3, d_3) → W_2
  55. Intersect(p_3, q_3) → Z_2
  56. Segment(W_2, Z_2) → f_5
  57. Polygon(A_3, B_3, 4) → poly19, g_5, h_5, i_5, j_5, C_3, D_3
  58. Polygon(B_3, E_3, 4) → poly20, k_5, l_5, m_5, n_5, F_3, G_3
  59. Polygon(E_3, H_3, 4) → poly21, p_5, q_5, r_5, s_5, I_3, J_3
  60. Polygon(D_3, C_3, 4) → poly22, t_5, a_5, b_5, c_5, K_3, L_3
  61. Polygon(C_3, F_3, 4) → poly23, d_5, e_5, f_6, g_6, M_3, N_3
  62. Polygon(F_3, I_3, 4) → poly24, h_6, i_6, j_6, k_6, O_3, P_3
  63. Polygon(L_3, K_3, 4) → poly25, l_6, m_6, n_6, p_6, Q_3, R_3
  64. Polygon(K_3, M_3, 4) → poly26, q_6, r_6, s_6, t_6, S_3, T_3
  65. Polygon(M_3, O_3, 4) → poly27, a_6, b_6, c_6, d_6, U_3, V_3
  66. Intersect(g_5, j_5) → W_3
  67. Intersect(p_5, q_5) → Z_3
  68. Segment(W_3, Z_3) → e_6
  69. Intersect(b_6, c_6) → A_4
  70. Segment(Z_3, A_4) → f_7
  71. Intersect(n_6, p_6) → B_4
  72. Segment(A_4, B_4) → g_7
  73. Segment(B_4, W_3) → h_7
  74. Intersect(i_5, j_5) → C_4
  75. Point(i_6) → D_4
  76. Segment(C_4, D_4) → i_7
  77. Intersect(i_6, j_6) → E_4
  78. Intersect(b_5, c_5) → F_4
  79. Segment(E_4, F_4) → j_7
  80. Intersect(g_5, h_5) → G_4
  81. Intersect(m_6, n_6) → H_4
  82. Segment(G_4, H_4) → k_7
  83. Intersect(k_5, l_5) → I_4
  84. Intersect(r_6, s_6) → J_4
  85. Segment(I_4, J_4) → l_7
  86. Intersect(i_2, j_2) → F
  87. Intersect(a_2, d_2) → G
  88. Segment(F, G) → i
  89. Midpoint(i) → H
  90. Intersect(i_3, j_3) → I
  91. Intersect(n_6, p_6) → K_4
  92. Segment(I, K_4) → j
  93. Midpoint(j) → L_4
  94. Line(L_4, p_4) → l

AI Drawing Prompt Reference

Draw a complex geometric model made up of multiple squares that are interconnected by edges and vertices, forming a three-dimensional structure. Start by drawing a vertical line segment as the base, then draw several squares on both sides of the line segment in sequence, connecting them one by one. Next, draw more squares using the vertices and edges of the existing squares, gradually expanding the structure. Finally, connect the edges and vertices of these squares to form a complex geometric shape.
The prompt above was compiled from the original drawing commands and is for reference only.